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Labour has demanded the government publish internal estimates about the effect of abolishing "non-dom" tax status.
The party says it wants ministers to "come clean" about the impact of keeping the "unfair" status ahead of the Budget on 15 March.
It says scrapping non-dom rules would bring in £3.2bn a year to spend on schools and the NHS.
But a Treasury minister said advice to ministers should remain confidential.
Responding to Labour's call, Financial Secretary to the Treasury Victoria Atkins added that ministers need to be able to receive "free and frank advice" from officials.
She added the government keeps all taxes under review, and would only announce changes during Budgets.
Labour wants to scrap non-dom status, which allows UK residents whose permanent homes are abroad not to pay British taxes on overseas income.
It announced the policy last year, saying it would replace the rule with a shorter-term scheme for temporary residents.
In November, Chancellor Jeremy Hunt said he had asked officials at the Treasury to "look into" how much scrapping the policy would raise, following claims from Labour.
On Tuesday, Labour used a motion in Parliament to call for the government to publish the findings before 28 February, two weeks before the spring Budget.
However, MPs voted 305 to 229 to reject the motion.
During the Commons debate, shadow Treasury minister James Murray said non-dom status was an "indefensible 200-year-old tax loophole", and getting rid of it was a "no brainer".
He added: "Labour believes that if a person makes Britain their home they should pay their taxes here. That patriotic point should be accepted on all sides of the political divide."
The SNP supported Labour's proposals, with the party's economic spokesman Stewart Hosie saying abolishing non-dom status was about "tax fairness".
But Ms Atkins said: "In developing policy, ministers must be able to have, if you like, a safe space to be advised by officials.
"That process should not play out in public, especially given the issues that Treasury ministers deal with are often highly market sensitive."
Last year it emerged that now-Prime Minister Rishi Sunak's wife Akshata Murty had non-dom status.
Ms Murty said she did not want the issue to be a "distraction" for her husband, who was chancellor at the time.