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Labour leader Sir Keir Starmer says the party will not be "influenced by threats" after its biggest backer said it may cut funding.
Unite union boss Sharon Graham has threatened to withdraw support over a council pay dispute in Coventry.
Sir Keir told the BBC's Laura Kuenssberg he was happy to debate merits of industrial disputes.
But he added he was "not going to be influenced by those who say we'll only provide money if you do 'x'."
Unite is Labour's single biggest donor, providing it with millions in funding every year.
It gave the party £3m in the run up to the last election in 2019.
But in 2020, under its former leader Len McCluskey - a close ally of ex-leader Jeremy Corbyn - the union decided to cut its affiliation money by about 10%.
More could now be withdrawn over the row in Coventry, which has seen a bitter dispute between the union and the Labour-run council over the pay of bin lorry drivers.
In a message to strikers, Unite's general secretary, Ms Graham, said: "Let me be very clear - the remaining financial support of the Labour Party is now under review."
Asked in the exclusive interview with the BBC's Political Editor if he was concerned by Ms Graham's comments, Sir Keir said: "The Labour Party I lead is not going to be influenced by threats from anybody, whoever they are, and that is just an absolute matter of principle for me.
"The merits of individual disputes I can debate all day, uphill and down dale.
"But I am not going to challenged and I am not going to be influenced by those who say we'll only provide money if you do 'x'."
Asked if he was concerned about wider unhappiness on the left wing of his party, Sir Keir said: "We have changed massively as a party in the last two years.
"My first task was to change the Labour Party [after] we lost very badly in 2019.
"What I am concerned with is not so much what our members think but what the public think, as it is the public we need to persuade to vote for us."
He added: "For every critical voice in the Labour Party, there are hundreds of supportive voices, because members of the Labour Party are in the Labour Party because they want to see a Labour government.
"That's what I'm focused on, that's what they are focused on and that's what we are putting all our energy and all our commitment into - facing up to the next general election [and] facing the public, not looking inwards and just having discussions in the Labour Party."