Labour’s Tom Watson said he had been “informed” that the now former international development secretary met British diplomats in Jerusalem during her visit there in August.
It follows a report that Number 10 told Ms Patel not to reveal meetings with foreign officials that she did not disclose in her first apology and clarification.
Downing Street categorically denies the claims.
But Mr Watson said if they are true, it would be “impossible” for the Foreign Office to claim it was unaware of Ms Patel’s presence in Israel.
He wrote in a letter to Mrs May: “The existence of such a meeting or meetings would call into question the official account of Ms Patel’s behaviour, and the purpose of her visit.
Mr Watson included nine questions – including why Ms Patel’s visit to consular official was not made public and if the Government “suppressed” information about her trip.
Downing Street did not respond to a request for comment from Sky News.
The questions come as Theresa May faced her second Cabinet resignation in a week – with Ms Patel following former foreign secretary Sir Michael Fallon out of Government.
Ms Patel, who had been touted as a future Tory leader, appeared to acknowledge she had breached the ministerial code in a resignation letter on Wednesday, offering the Prime Minister a “fulsome apology”.
The former international development secretary had said that her actions “fell below the high standards” of ministerial office and that while she acted with the best of intentions, they “fell below the standards of transparency and openness that I have promoted and advocated”.
Mrs May said in her response that “it is right you have decided to resign”.
Ms Patel had been under scrutiny after failing to inform either the Foreign Office or Downing Street about 12 meetings she held with top officials during a 13-day “family holiday” to Israel in August.
In fresh revelations, it is understood Ms Patel met Israel’s public security minister Gilad Erdan in Parliament on 7 September and foreign ministry official Yuval Rotem in New York on 18 September.
Downing Street sources denied reports Ms Patel was told not to reveal her meeting with Mr Rotem in a list she published earlier this week.