Rishi Sunak should not be involved in any decision about reforming “non-dom” tax rules given the “clear conflict of interest” presented by his wife’s status, Labour has argued.

The party’s shadow attorney general Emily Thornberry stepped up pressure on the chancellor after he described the scrutiny of his multi-millionaire spouse Akshata Murty’s financial affairs as a “smear”.

Meanwhile, the focus on Mr Sunak has widened as Sky News has been told that the MP and his wife held US green cards – permitting him residence in the country – until more than a year into his time at 11 Downing Street.

Green card holders must pay US tax on their worldwide income and pledge that the US is their forever home. A source close to Mr Sunak said neither he nor his wife have green cards but refused to say if they had them during any of his time as chancellor.

Labour’s shadow chief secretary to the Treasury Pat McFadden said there “must be transparency on this question of the green card”.

The issue of Ms Murty’s non-dom status was first confirmed after being reported by the Independent earlier this week

Having the status enables Ms Murty, the Indian-born daughter of a billionaire tech boss, to reduce her tax liability – and means her permanent home is considered to be outside the UK despite the Sunaks living in Downing Street.

Ms Murty, who owns a 0.9% stake worth hundreds of millions of pounds in her father’s company Infosys, pays an annual levy of £30,000 to the UK government to keep her non-dom status, her spokeswoman has confirmed.

Mr Sunak has bristled over scrutiny of his wife’s tax affairs, telling the Sun newspaper in an interview that: “To smear my wife to get at me is awful.”

The chancellor won support in some quarters, with energy minister Greg Hands telling LBC that the attention on Ms Murty was “a little bit unpleasant”.

Tobias Ellwood, a senior Tory backbencher who has been critical of the prime minister recently, also called for the focus to shift away from the chancellor’s wife but did tell Sky News that the rules on non-dom status were “out of date” and needed to be reviewed.

But Ms Thornberry said: “There is a clear conflict of interest here because the chancellor of the exchequer is responsible for the rules on non-doms.

“He has a wife who made a positive decision to become a non-dom, which meant that she doesn’t pay tax on her worldwide income but only on her income in the UK.”

She suggested that while what Mr Sunak’s wife has done is “perfectly legal”, it was questionable whether it was fair given the rising tax burden being imposed on the British public, adding: “He’s expecting us all to pull our weight but not his partner.”

Ms Thornberry said: “He should have declared that his wife was a non-dom because he’s responsible for the rules on non-doms.

“If you look at the details, it does seem a bit odd sometimes – she’s been here eight years, she’s got kids, she’s living in Downing Street in a taxpayers’ flat, but she’s not here as a permanent resident. It does seem odd.

“It may be that they may have had discussions in the Treasury about updating these rules, making sure they’re more relevant.

“Would he have been involved in those discussions? He shouldn’t have been and he should have declared that he had a conflict of interest.”

The chancellor has come out fighting after the Labour leader Sir Keir Starmer accused him of “breath-taking hypocrisy” over his Indian-born wife’s status as a “non-dom”.

That means, because she is an Indian citizen she does not have to pay UK tax on income from foreign investments or earnings, but pays UK taxes on her UK income.

Mr Sunak told the Sun his wife had done nothing wrong or broken any rules but had followed the letter of the law.

“Every single penny that she earns in the UK she pays UK taxes on, of course she does,” he said.

“And every penny that she earns internationally, for example in India, she would pay the full taxes on that.

“That is how the system works for people like her who are international who have moved here.”