Conservative MP Alicia Kearns has raised concerns over whether Jonathan Powell, the National Security Advisor, can remain in his post following his wife's references to Palestine Action on social media.
The shadow home affairs minister has written to the prime minister questioning whether Powell's position is still tenable, despite the Metropolitan Police concluding no action was necessary over his wife's, Sarah Helm, comments.
A Downing Street spokeswoman told the BBC: "These views are held by an individual who does not represent the government in any capacity."
Posting on X last Thursday, Helm wrote: "God help us authors who support Palestine and Palestine Action," responding to a discussion about the author Sally Rooney.
The Normal People writer announced last week that her books will not be supplied to UK booksellers after she announced she would use her royalties to support Palestine Action.
The Met investigation into Helm's post found "it did not meet the criminal threshold" and the matter was dropped on Saturday.
But Kearns has written to Andy Burnham about the handling of sensitive national security information, asking whether the government has investigated the posts and whether he retains full confidence in his adviser.
She told the BBC: "We cannot have the NSA's wife tweeting about what decisions her husband has or hasn't made."
Palestine Action was proscribed as a terror organisation last year, making it a a criminal offence punishable by up to 14 years imprisonment to belong to or support the group.
An appeal against the proscription of Palestine Action is due to be heard by the Supreme Court next month, external, in a battle that has now gone on for more than year.