Theresa May is facing pressure to reveal what the Foreign Office knew about Priti Patel's secret meetings with Israeli politicians.
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.
Mr Watson told Sky News he took a call from Israel on Wednesday, from someone who wishes to remain anonymous, who claimed the Foreign Office asked Downing Street not to publish details of this meeting.
"If that is the case it shows that at some point the public has not been given the full facts of this case," he said.
The deputy Labour leader wants to "establish the facts" of Ms Patel's trip before discovering the "motive" of the alleged cover-up.
It follows another 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 those claims.
Five questions that still need answering over Priti Patel's Israel trip:
:: What and when did the Foreign Office know?
Labour's Tom Watson claims Ms Patel met British diplomats in Jerusalem during her trip, meaning the Foreign Office must have been aware she was in the region. Could she have been acting on Mrs May's authorisation? Why was her meeting with UK officials not made public?
:: What did Downing Street know?
The Jewish Chronicle alleges Downing Street was aware of Ms Patel's meeting with Israeli PM Benjamin Netanyahu "within hours", as well as her September talks with a top Israeli foreign ministry official. The latter meeting ultimately led to her downfall. Number 10 denies the claims.
:: Did Ms Patel visit the Golan Heights?
Israeli newspaper Hareetz claims Ms Patel visited an Israeli military hospital in the occupied Golan Heights during her trip, which would represent a major breach of UK diplomatic protocol.
:: What was the role of Lord Polak?
Tory peer Lord Polak, an influential lobbyist, arranged all of Ms Patel's meetings in Israel and sat in on all but one of them.
:: Why was Ms Patel there?
It has been suggested the ambitious MP's real motivation for making the trip to Israel was to win favour with influential Tory donors, via Lord Polak's connections. Ms Patel has been frequently touted as a future party leader.
Mr Watson said if the claims he has heard are true, it would be "impossible" for the Foreign Office to claim it was unaware of Ms Patel's presence in Israel.
In a letter to Mrs May on Wednesday, he wrote: "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 Mrs May faced her second Cabinet resignation in a week - with Ms Patel following former defence secretary Sir Michael Fallon out of Government.
On Thursday morning, after her resignation, Ms Patel posted on Twitter: "An enormous thank-you to friends, colleagues, constituents & the public for the support & kindness you have shown me over the last few days."
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 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 the reports Ms Patel was told not to reveal her meeting with Mr Rotem in a list she published earlier this week.