Asked if he would do a deal with the Lib Dems, the Labour leader told the BBC this was a "hypothetical question".

But he said he would never do a deal with the SNP because of a "fundamental disagreement" on Scottish independence.

Despite local election gains, experts say support for Labour may not yet be enough to win an overall majority.

Last week the party gained 537 councillors and 22 councils in England, including key battlegrounds like Swindon, Plymouth, Medway and Stoke-on Trent.

Those are places where Labour is hoping for success at the next general election.

Following the results, Sir Keir said his party was on course for a majority.

The BBC's projected national share - which estimates what the outcome would have been if all of Britain had the chance to vote - put Labour at 35%, nine points ahead of the the Conservatives.

But many commentators have predicted this level of support may not translate into an overall majority at the next general election, which must happen before January 2025.

If no party wins a majority in the House of Commons, the result is a hung Parliament.

The party with the most seats is usually asked to form a government but in order to secure a majority it must get support from other parties - either through an informal deal or a formal coalition.

Asked if he would ever do a deal with the Liberal Democrats, Sir Keir told the BBC: "I want to press on for a Labour majority, that's what we're aiming for. This is a hypothetical question."

However, in response to the same question in relation to the Scottish National Party, he said: "No... because there's a fundamental disagreement.

"I will never do a deal with a party that thinks the separation of the United Kingdom is the way forward."

Put to him that this was also a hypothetical question, Sir Keir insisted "there is no basis for a deal at all with the SNP because of their politics of separation".

On Sunday, Lib Dem leader Sir Ed Davey - whose party gained 12 councils and more than 400 councillors on Thursday - ruled out going into a coalition with the Conservatives but refused to say the same for Labour.

He said it was a "hypothetical question" adding that he would not "take the voters for granted".

On Tuesday, he added that the party's strategy was to target Conservatives in so-called "blue wall" areas of southern England and there must be "no sitting back".

It all adds up to what looks like symmetrical flirting from Labour and the Liberal Democrats.

They each answer the question in exactly the same way, despite being able to be categoric about equally hypothetical situations of deals with the Conservatives and the SNP respectively.

In both local elections and at a general election, in most instances Labour and the Lib Dems are competitive against the Conservatives in different parts of the country.

Expect to see Tory MPs and ministers talk up what they see as the dangers of a hung parliament, with Labour reliant on other parties for support.

In 2010, the Lib Dems formed a coalition government with the Tories but the party paid the price at the next general election, losing 49 seats.

The Conservative-Lib Dem coalition lasted a full term and was arguably more stable than the Conservative-only governments that followed it.

Sir Keir said he was "confident" Labour's local election results put the party on course for a majority but he was not "complacent", saying "there's more work to do".

The Labour leader added that his party's campaign had focused on tackling the cost of living and it now needed to "deliver".

Leaders of the 22 councils won by Labour have been given the job of drawing up "emergency cost-of-living plans" within their first 100 days, as well as reviewing local housing and development policies.

Sir Keir was also asked if he agreed with comments made by Labour's then-Business Secretary Peter Mandelson at the height of the New Labour government under Tony Blair, that he was "intensely relaxed about people getting filthy rich as long as they pay their taxes".

"I'm very relaxed about people being rich and getting rich," Sir Keir said.

"I know what aspiration is. I came from a working class background and I was able to not only head up the Crown Prosecution Service but now lead the Labour Party."

He added: "But I want, obviously, everyone to pay their taxes and I want fairness and I want equality and I want every child to have that opportunity."

Meanwhile, Prime Minister Rishi Sunak has insisted his five priorities - including cutting inflation, bringing down NHS waiting lists and tackling small boat crossings - are the best way to put his party back on track after it lost 48 councils and more than 1,000 councillors.