Donald Trump on Wednesday refused again to publish his tax returns after a conservative pundit suggested they might link him to Russia.

The Republican candidate has refused for months to publish the returns while an IRS audit is ongoing.

He was questioned about the refusal at a press conference in Miami, and doubled down, saying that his position was unchanged.

Scroll down for video

Why won't he release them? Trump was asked again about his tax returns on Wednesday and continues to insist he will release them once an audit is completed

Link? George Will (left), the conservative pundit who is leaving the Republican party over Trump's candidacy, suggested the Russian involvement, while Supreme Court Justice Ruth Bader Ginsburg (right) has questioned why he hasn't published them

But he is now facing claims that the returns are being withheld because they will show he has links to Russia - which he fiercely denies.

The link was posted by conservative pundit George Will, who The Hill reported had told Fox News' Bret Baier of his suspicion on Tuesday.

Will, who is leaving the Republican party over Trump's candidacy, said: 'Perhaps one more reason why we're not seeing his tax returns - because he is deeply involved in dealing with Russian oligarchs and others.

'Whether that's good, bad or indifferent, it's probably the reasonable surmise.'

Trump on Wednesday came under pressure from a reporter at the press conference on the returns.

'I'll release when the audit's completed,' he said.

'Nobody would release when it's under - I've had audits for 15 or 16 years.

'Every year I have a routine audit. I'm under audit, when the audits complete I'll release them.

'And as far as the tax returns, as soon as the audits complete, like any lawyer would tell you, Greta Van Susteren she was going over it a while ago, she's a lawyer.

'She said well no lawyer would let somebody release a tax return when they're under audit.'

Trump also repeatedly denied having any link to Russia, a claim which has been raised in the wake of the hacking of the Democratic National Committee emails.

President Obama has been the most prominent voice to claim that Russia was likely to be behind the attacks - which led to the resignation in disgrace of DNC chair Debbie Wasserman Schultz - and link them to Trump.

'What the motives were in terms of the leaks, all that – I can't say directly,' Obama told NBC News.

'What I do know is that Donald Trump has repeatedly expressed admiration for Vladimir Putin.'

Claims of a link to Russia in a tax return were questioned by one expert.Jeremy Scott, a federal tax expert, told CNN Money that it was extremely unlikely that business links would be revealed in the IRS documentation.

'You'll learn a little bit more, but you won't see any direct dealings with Russian oligarchs,' he said.

The calls for the returns to be published were renewed earlier this month from the unlikely quarter of the Supreme Court.

Ruth Bader Ginsburg, who said she was speaking in a personal capacity, she told CNN's legal analyst Joan Biskupic: 'How has he gotten away with not turning over his tax returns? The press seems to be very gentle with him on that.'