Rishi Sunak is “deeply concerned” about a potential Israeli offensive in the city of Rafah in the south of Gaza.

It comes after Israel’s military told Palestinians to leave parts of the city, with the announcement appearing to signal a long-threatened Israeli ground invasion is imminent.

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Speaking on Monday, Mr Sunak said: “I’ve been very consistent that we are deeply concerned about the prospect of a military incursion into Rafah, given the number of civilians that are sheltering there and the importance of that crossing for aid.

“I’ve made those points repeatedly to Prime Minister Netanyahu.

“The priority right now should be on all parties, but particularly Hamas, to agree to a deal to release hostages and allow more aid to go in as part of a temporary pause, which will allow us to build a sustainable ceasefire.

“That’s the best way to end the suffering. And that’s what I continue to call on all parties to do.”

Labour leader Sir Keir Starmer has said an Israeli offensive “must not go ahead”, while shadow foreign secretary David Lammy called for an “immediate ceasefire” and said an Israeli offensive in Rafah “would be catastrophic”.

Israel says Rafah is the last significant Hamas stronghold but had previously paused plans to attack the city in southern Gaza so hostage release negotiations could take place.

However, Israeli defence minister Yoav Gallant claimed on Sunday that Hamas was not serious about a deal and the army was preparing “a powerful operation in the very near future in Rafah”.

On Sunday, Hamas set off rockets from Rafah towards Kerem Shalom, Israel’s main crossing point for delivering aid, killing three Israeli soldiers.

Overnight, Israeli strikes killed at least 19 people, including a baby, according to Palestinian health officials.

Follow live updates from the Israel-Hamas war

Israel’s army has told about 100,000 people to evacuate eastern Rafah to a humanitarian zone designated by Israel on the Mediterranean coast.

Rafah, Gaza’s most southern city, on the Egyptian border, is where more than a million people – more than half of Gaza’s population – have taken refuge during the war that began last October.

Joining other Western nations and humanitarian organisations in urging Israel not to strike Rafah, Sir Keir said on social media: “With more than a million Palestinian civilians sheltering in Rafah, an Israeli offensive must not go ahead.

“There must be an immediate ceasefire, the immediate release of all hostages, and unimpeded aid into Gaza that can be delivered regularly, quickly and safely.”

Read more: Why has Israel’s offensive prompted widespread international condemnation?

Mr Lammy wrote: “An Israeli offensive in Rafah would be catastrophic. It must not go ahead.

“We need an immediate ceasefire, the immediate release of hostages, and immediate unimpeded aid to Gaza.”

UK Foreign Secretary Lord Cameron earlier said the UK is “very concerned” about the situation in Rafah and called for Israel to “stop and think seriously” before taking further action.

Charity ActionAid said forcing Palestinians from Rafah “without a safe destination is not only unlawful but would lead to catastrophic consequences”.

They said “there are no safe zones in Gaza” and aid workers have seen some of the “most severe conditions in recent memory” with widespread disease, starvation and chaos.

Madeleine McGovern, from Care International UK, said ministers need to urgently suspend licences for arms sales to Israel to prevent an expansion of military operations in Rafah.

“It would be unconscionable for British-made weapons to be used in an assault on Rafah,” she said.

Islamic Relief warned the area where Palestinians have been ordered to move, al Mawasi, is not safe and that forcing more people there will make the humanitarian crisis worse.

The results of the next general election are not a “foregone conclusion” according to Rishi Sunak, after his party’s slate of defeats in the local elections.

The prime minister was speaking off the back of analysis of the results conducted by Sky News which indicated the country was heading towards a hung parliament.

This projection, however, does not account for Labour now being the most popular party in Scotland, nor does it recognise that people are less likely to vote for an independent or small party in a Westminster election when compared to council seats.

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Speaking from a charity in north London, Mr Sunak said: “Well, the independent analysis shows whilst of course, this was a disappointing weekend for us, that the result of the next general election isn’t a foregone conclusion and indeed actually is closer than the situation is closer than many people are saying.”

Mr Sunak also paid tribute to the almost 500 Tory councillors who were unseated over the weekend, as well as West Midlands mayor Andy Street.

“Well, obviously disappointing to lose Conservative councillors and a fantastic mayor for the West Midlands in Andy Street,” the prime minister said.

“And I’m grateful to them for their public service and all their hard work.

“For my part, reflecting on it, I’m determined more than ever to demonstrate to the country that we are making progress on the areas that matter to them, and we are going to deliver for them.”

Asked about the disquiet from within his party about the direction the Conservatives are taking, Mr Sunak said: “What unites all members of our party, MPs and beyond, are our values as Conservatives and the type of country that we want to build.”

In the wake of the local election defeats, Mr Sunak was facing calls to tack both further right and further to the centre.

Mr Street called on the prime minister not to drift to the right, telling Sky News that he “would definitely not advise that drift”.

“The message is clear: winning from that centre ground is what happens,” he added.

Meanwhile, former home secretary Suella Braverman wrote in the Daily Telegraph that “the hole to dig us out of is the PM’s, and it’s time for him to start shovelling”.

She called for the Conservatives to take a tougher stance on tax, migration, small boats and law and order.

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Mr Sunak said: “I’m absolutely determined to fight incredibly hard for what I believe and for the future country that I want to build, and that’s what I’m going to do.

“Fight for this country, fight for the things I believe and deliver for everyone on the things that matter to them.”