Ms Truss said she was “incredibly sorry” to lose her good friend Mr Kwarteng, and confirmed that she had appointed Jeremy Hunt in his place.
She said Mr Hunt would deliver the medium-term fiscal plan at the end of the month.
Ms Truss also confirmed the government would raise corporation tax next April to 25% from 19%, despite pledging not to do so in the mini-budget.
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The PM spoke for just three and a half minutes and answered only four questions from journalists, for which she has received much criticism, with some Tory MPs saying the news conference only made things worse.
Ms Truss said Mr Hunt is “one of the most experienced and widely respected government ministers and parliamentarians, and he shares my convictions and ambitions for our country”.
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But she refused to take responsibility for any of the economic turmoil the mini-budget caused, saying: “It is clear that parts of our mini-budget went further and faster than markets were expecting, so the way we are delivering our mission now has to change.”
Determined to remain as prime minister, she said she “acted decisively” and in the national interest.
“I am determined to see through what I’ve promised – deliver higher growth, a more prosperous United Kingdom,” she insisted.
“I have to act in the national interest as prime minister.”
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Moment PM abruptly ends news conference
And asked if she would apologise after former Tory chancellor Philip Hammond said she had trashed the party’s winning reputation for economic competence, she refused.
“Well, I am determined to deliver on what I set out when I campaigned to be party leader,” she said.
“We need to have a high growth economy, but we have to recognise that we are facing very difficult issues as a country.”
Image: Jeremy Hunt has replaced Kwasi Kwarteng as chancellor
The PM sacked Mr Kwarteng this afternoon, shortly after he landed in London after leaving International Monetary Fund meetings in Washington DC early.
He was sacked three weeks after unveiling £45bn of unfunded tax cuts in the mini-budget, which pushed the pound to a record low against the dollar, sent the cost of government borrowing and mortgage rates up and led to an unprecedented intervention by the Bank of England.
The economic turmoil forced the government into two U-turns of major policies in the mini-budget: abolishing the 45p rate of income tax for higher earners and axing the planned rise in corporation tax from 19% to 25% next April.
At least 20 people have been killed and dozens more injured after an Israeli airstrike targeting a school in Gaza, health authorities have said.
Reuters news agency reported the number of dead, citing medics, with the school in the Daraj neighbourhood having been used to shelter displaced people who had fled previous bombardments.
Medical and civil defence sources on the ground confirmed women and children were among the casualties, with several charred bodies arriving at al Shifa and al Ahli hospitals.
The scene inside the school has been described as horrific, with more victims feared trapped under the rubble.
This breaking news story is being updated and more details will be published shortly.
Donald Trump has threatened Russia with more sanctions after a series of deadly strikes across Ukraine, as he said of Vladimir Putin: “What the hell happened to him?”
Speaking to reporters at an airport in New Jersey ahead of a flight back to Washington, Mr Trump said: “I’m not happy with Putin. I don’t know what’s wrong with him.”
“He’s killing a lot of people,” he added. “I’m not happy about that.”
Mr Trump – who said he’s “always gotten along with” Mr Putin – told reporters he would consider more sanctions against Moscow.
“He’s sending rockets into cities and killing people, and I don’t like it at all,” he said.
Ukraine said the barrage of strikes overnight into Sunday was the biggest aerial attack of the war so far, with 367 drones and missiles fired by Russian forces.
It came despite Mr Trump repeatedly talking up the chances of a peace agreement. He even spoke to Mr Putin on the phone for two hours last week.
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2:38
Hundreds of drones fired at Ukraine
‘Shameful’ attacks
Volodymyr Zelenskyy has said Ukraine is ready to sign a ceasefire deal, and suggested Russia isn’t serious about signing one.
In a statement after the latest attacks on his country, he urged the US and other national leaders to increase the pressure on Mr Putin, saying silence “only encourages” him.
Mr Trump’s envoy for the country, Keith Kellogg, later demanded a ceasefire, describing the Russian attacks as “shameful”.
Three children were among those killed in the attacks, explosions shaking the cities of Kyiv, Odesa, and Mykolaiv.
Image: Ukrainian siblings Tamara, 12, Stanislav, eight, and Roman, 17, were killed in Russian airstrikes. Pic: X/@Mariana_Betsa
Before the onslaught, Russia said it had faced a Ukrainian drone attack on Sunday. It said around 100 were intercepted and destroyed near Moscow and in central and southern regions.
The violence has escalated despite Russia and Ukraine completing the exchange of 1,000 prisoners each over the past three days.
Donald Trump says he will delay the imposition of 50% tariffs on goods entering the United States from the European Union until July, as the two sides attempt to negotiate a trade deal.
It comes after the president of the European Commission, Ursula von der Leyen, said in a post on social media site X that she had spoken to Mr Trump and expressed that they needed until 9 July to “reach a good deal”.
But Mr Trump has now said that date has been put back to 9 July to allow more time for negotiations with the 27-member bloc, with the phone call appearing to smooth over tensions for now at least.
Speaking on Sunday before boarding Air Force One for Washington DC, Mr Trump told reporters that he had spoken to Ms Von der Leyen and she “wants to get down to serious negotiations” and she vowed to “rapidly get together and see if we can work something out”.
The US president, in comments on his Truth Social platform, had reignited fears last Friday of a trade war between the two powers when he said talks were “going nowhere” and the bloc was “very difficult to deal with”.
Mr Trump told the media in Morristown, New Jersey, on Sunday that Ms Von der Leyen “just called me… and she asked for an extension in the June 1st date. And she said she wants to get down to serious negotiation”.
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“We had a very nice call and I agreed to move it. I believe July 9th would be the date. That was the date she requested. She said we will rapidly get together and see if we can work something out,” the US president added.
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0:54
12 May: US and China reach agreement on tariffs
Much of his most incendiary rhetoric on trade has been directed at Brussels, though, even going as far as to claim the EU was created to rip the US off.
Responding to his 50% tariff threat, EU trade chief Maros Sefcovic said: “EU-US trade is unmatched and must be guided by mutual respect, not threats.