Image copyright Getty Images Image caption Len McCluskey has been a vocal supporter of Jeremy Corbyn

Jeremy Corbyn could step down if Labour's fortunes do not improve before the next general election in 2020, one of his closest allies has suggested.

Len McCluskey, head of the Unite union, described the party's standing in the opinion polls as "awful".

He said Mr Corbyn and shadow chancellor John McDonnell were not "desperate to cling onto power for power's sake".

A Unite leadership rival accused him of issuing a "public ultimatum" and trying to be "Labour's puppet master".

Gerard Coyne, one of two challengers to Mr McCluskey for the job of Unite general secretary, said Mr McCluskey was focusing on party politics over the union's membership.

The spat between the Unite rivals came after Mr McCluskey told the Daily Mirror the union's leadership contest was being used by Mr Corbyn's critics as a "proxy war" against the party leader.

As Unite leader, he said, he offered "critical support" to Mr Corbyn.

He added: "Let's suppose we are not having a snap election.

"It buys into this question of what happens if we get to 2019 and opinion polls are still awful.

"The truth is everybody would examine that situation, including Jeremy Corbyn."

On Mr Corbyn and Mr McDonnell, he added: "These two are not egomaniacs, they are not desperate to cling onto power for power's sake."

McCluskey fighting his own election

By Chris Mason, BBC political correspondent

Len McCluskey is a huge figure in the Labour movement and was an early, vocal and influential advocate of Jeremy Corbyn becoming - and then remaining - the party's leader.

So why is he saying this now?

These remarks have to be seen through the prism of yet another election: Mr McCluskey attempting to remain Unite's leader, and facing an opponent who says he spends too much time talking about Westminster politics.

As well as the comments about Jeremy Corbyn's possible sell-by date, there is another telling line from Len McCluskey today.

"It's my job to promote Unite's policies, not Labour's," he says.

Mr McCluskey has votes to win for himself right now, not votes to win for Jeremy Corbyn.

Later, on Twitter, Mr McCluskey said Mr Corbyn "continues to have my full support", describing him as a "genuine, decent man fighting for a fairer Britain".

"Media headlines distort facts", he added.

Mr Coyne, Unite's West Midlands secretary, said: "I am astonished and deeply concerned that, at a time like this, Len McCluskey should deliver what amounts to a public ultimatum to the leader of the Labour Party.

"My criticism of his handling of the role of general secretary of Unite is not whether he has backed the right leader or the wrong leader of the Labour Party, but that he appears to think it is his job to be Labour's puppet master."

This drew an angry response from Mr McCluskey, who said the "puppet master" comment "panders to the worst anti-Labour stereotypes of the media".

In a reference to MPs who have opposed Mr Corbyn, Mr McCluskey claimed Mr Coyne's campaign was being "scripted by the failed plotters in the Parliamentary Labour Party, for whom Unite would be collateral damage in their political project to bring back Blairism".

Immigration debate

In his Mirror interview, Mr McCluskey also said Labour had to show "ordinary people" it was "listening to their concerns" on immigration, saying it had to "get its narrative right on free movement".

Mr Corbyn has defended the principle of free movement and declined to offer "false promises" on migration numbers.

But others in his party have said the system must change in light of the Brexit vote.

Mr Coyne focused on Brexit in a speech in Birmingham, warning that new immigration controls had to be "non-negotiable" when talks between the UK and the EU get under way.

Unite members who voted for Brexit expected a promise of an end to uncontrolled immigration from the EU to be kept, "and will feel betrayed if it is not", he said.

Ian Allinson, the third candidate in the leadership contest, accused Mr Coyne of making an "irresponsible" pitch for votes, and said Mr McCluskey had "fudged" the question of free movement.

"Scapegoating immigrants weakens our union and hinders our efforts for jobs, pay and conditions," he said.

The new Unite leader will be announced on 28 April.