The prime minister wants to deliver a stronger NHS and the “sentiment remains people should not be missing appointments”, according to his spokesperson.
But they added: “We have listened to GPs and NHS leaders and agreed now is not the time to take this policy forward.”
Mr Sunak visited Croydon University Hospital in south London on Friday, where he was asked about nurses’ pay.
Research commissioned by the Royal College of Nursing suggested that they are working an extra day a week for no more pay.
The data also suggests their wages have fallen 20% in real terms, based on a five-day week.
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0:30
Patient confronts PM on pay for nurses
PM dodges salary question on hospital visit
Dodging a question on nurses’ salaries, Mr Sunak said: “It is brilliant to be here at Croydon Hospital, to see the great work of the doctors and nurses here.
“One of the priorities for my government is going to be tackling the COVID backlogs and supporting the NHS.
“We face lots of challenges as a country, but I am confident that we can fix the economy and deliver on the promise of the 2019 manifesto, including having a stronger NHS.”
The PM was confronted by 77-year-old Catherine Poole, a patient, who said it was a “pity you don’t pay them more”.
Mr Sunak replied by saying: “We’re trying,” to which she said: “You need to try harder.”
As chancellor, Mr Sunak brought in a 1.25% increase in National Insurance to help pay for fixing COVID backlogs in health and social care.
His predecessor Liz Truss reversed the measure because of the cost-of-living crisis.
Speaking to reporters in front of his residence at Rideau Cottage, in the country’s capital, Ottawa, he said “internal battles” mean that he “cannot be the best option” in the next election.
“I don’t easily back down faced with a fight, especially a very important one for our party and the country. But I do this job because the interests of Canadians and the well-being of democracy is something that I hold dear.
“A new prime minister and leader of the Liberal Party will carry its values and ideals into that next election. I am excited to see that process unfold in the months ahead.”
Former governor of the Bank of England, Mark Carney, is among the favourites to succeed him.
Chrystia Freeland, whose stunning resignation as finance minister and deputy prime minister precipitated the current crisis, leads in the polls.
Other front-runners are the former premier of British Columbia, Christy Clark, current finance minister Dominic LeBlanc and minister of foreign affairs, Melanie Joly.
Mr Trudeau, who has been prime minister since 2015, faced calls to quit from a chorus of his MPs amid poor showings in opinion polls.
He came under further pressure after Ms Freeland quit in December because of policy disagreements, including over how to handle possible US tariffs imposed by Donald Trump‘s incoming administration.
Mr Trudeau’s resignation comes as the polls show his party is likely to suffer a heavy defeat to the official opposition Conservatives in an election that must be held by late October.
The Liberals must now name an interim leader to take over as prime minister ahead of a special leadership convention.
Mr Trudeau came to power 10 years ago following a decade of Conservative Party rule and was initially praised for returning the country to its liberal past.
But he has become deeply unpopular with voters in recent years over a range of issues, including the soaring cost of food and housing and surging immigration.
He is the eldest son of Pierre Trudeau, one of Canada’s most famous prime ministers, who led the country from 1968 to 1979 and from 1980 to 1984.
The political upheaval comes at a difficult moment for Canada internationally.
US President-elect Donald Trump has threatened to impose 25% tariffs on all Canadian goods if Ottawa does not stem what Mr Trump calls a flow of migrants and drugs into the US.
Many fewer of each cross into the US from Canada than from Mexico, which Mr Trump has also threatened.
Speaking to reporters in front of his residence at Rideau Cottage, in the country’s capital, Ottawa, he said “internal battles” mean that he “cannot be the best option” in the next election.
“I don’t easily back down faced with a fight, especially a very important one for our party and the country. But I do this job because the interests of Canadians and the well-being of democracy is something that I hold dear.
“A new prime minister and leader of the Liberal Party will carry its values and ideals into that next election. I am excited to see that process unfold in the months ahead.”
Mr Trudeau, who has been prime minister since 2015, faced calls to quit from a chorus of his MPs amid poor showings in opinion polls.
He came under further pressure after his finance minister, Chrystia Freeland, resigned in December over clashes on policy.
The disagreements included how to handle possible US tariffs imposed by Donald Trump‘s incoming administration.
Mr Trudeau’s resignation comes as the polls show his party is likely to suffer a heavy defeat to the official opposition Conservatives in an election that must be held by late October.
The Liberals must now name an interim leader to take over as prime minister ahead of a special leadership convention.
Mr Trudeau came to power 10 years ago following a decade of Conservative Party rule and was initially praised for returning the country to its liberal past.
But he has become deeply unpopular with voters in recent years over a range of issues, including the soaring cost of food and housing and surging immigration.
He is the eldest son of Pierre Trudeau, one of Canada’s most famous prime ministers, who led the country from 1968 to 1979 and from 1980 to 1984.
The political upheaval comes at a difficult moment for Canada internationally.
US President-elect Donald Trump has threatened to impose 25% tariffs on all Canadian goods if Ottawa does not stem what Mr Trump calls a flow of migrants and drugs into the US.
Many fewer of each cross into the US from Canada than from Mexico, which Mr Trump has also threatened.
Few one-time golden boys manage to retain their lustre long into political office.
Barack Obama just about held on to his, leaving the US presidency with his approval rating high despite his party’s 2016 loss to Donald Trump.
But Emmanuel Macron is faltering in France and Justin Trudeau steps down as head of Canada’sliberal party with his popularity in shreds. So much for Western liberal values.
In the high tides of inflation and immigration, those who were their supposed flag-bearers are no longer what electorates want.
For Mr Trudeau, it is a dramatic reckoning. His approval ratings have dropped from 65% at their highest in September 2016 to 22% now, according to the “Trudeau Tracker” from Canada’s non-profit Angus Reid Institute.
The sudden departure of his finance minister and key political ally Chrystia Freeland last month dealt his leadership a body blow, just as Canada readies itself for a potential trade war with the US which, she argued in a bracing resignation letter, his government was not taking seriously enough.
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1:31
“Parliament has been paralysed for months,” Trudeau says
The man Mr Trump recently trolled as “Governor of the ‘Great State of Canada’ or ’51st (US) state'”, Mr Trudeau was as close to Canadian political royalty as it gets.
The son of the country’s 15th prime minister, Pierre Trudeau, he was famously toasted by US president Richard Nixon as “the future prime minister of Canada” when he joined his father on a state visit as a toddler.
Aged five, he met the late Queen for the first time. “Thank you for making me feel so old”, she remarked drily at a re-meet in Malta almost 40 years later.
He has led Canada’s liberal party since 2013 and served as the country’s 23rd prime minister for almost a decade.
Mr Trudeau won a resounding electoral victory in 2015 and secured the premiership through two subsequent elections, though as head of a minority government.
He made significant inroads against poverty in Canada, worked hard on nation to nation reconciliation with Canada’s indigenous communities, secured an effective trade deal with the US and Mexico in 2016 and managed to keep the public mostly on-side through the COVID-19 pandemic.
But he was a polarising figure. Holidays in exotic climes like a trip to the Bahamas in 2016 to an island belonging to the Aga Khan made him seem elitist and out of touch.
There was embarrassment when blackface images surfaced from his early years as a teacher, for which he apologised profusely.
His supposed liberal credentials smacked of double standards when he invoked emergency powers to crush truckers’ protests in 2022.
But it was the economic aftermath of the pandemic, with Canada suffering an acute housing shortage, immigration leaping under his premiership and the cost of living hitting households across the board which really piled on the pressure.
In those, Canada is not unique. But the opposition conservatives and the public at large clearly want change, and Mr Trudeau has responded.
He has announced his intention to resign as party leader and prime minister after the Liberals selects their next leader.
Mr Trudeau’s legacy may shine brighter with a little hindsight. But now is not that moment.
The question is whether his conservative opposition will fare any better in an increasingly combative geopolitical environment if, as seems likely, a candidate of their choosing wins a federal election due at some point this year.