After meeting Theresa May, the prime minister's office released Patel's resignation letter in which she apologised for causing "a distraction" from the work of government. May responded in a letter to say she believed Patel's decision was "right".
Patel had apologised on Monday for holding 12 separate meetings -- including with Prime Minister Benjamin Netanyahu -- during a family holiday to Israel in August, without notifying the Foreign Office or Downing Street in advance.
After a public reprimand from the prime minister, Patel left the UK on Tuesday for a three-day trip to Uganda, but returned to London's Heathrow Airport on Wednesday at May's request.
If she is sacked, Patel would become the second cabinet minister in a week to leave May's government, after Michael Fallon quit as defence secretary on November 1 following allegations of sexual harassment.
Britain is facing a major challenge in Brexit, but May has struggled to keep her ministers in line since losing her Conservative parliamentary majority in a snap election in June.
Months of public divisions over the negotiations with the European Union have in recent days given way to scandals over foreign affairs and sexual abuse.
May's deputy Damian Green is being investigated for allegedly groping a journalist in 2014 -- which he denies -- while a similar probe is under way into the behaviour of junior trade minister Mark Garnier towards his secretary.
Meanwhile, Foreign Secretary Boris Johnson has been accused of jeopardising the case of a British woman jailed in Iran, after appearing to suggest she was training journalists at the time -- something her family strongly denies.
May put off a mooted reshuffle after her election setback, but some MPs have called on her to act to assert her power over a government that looks increasingly adrift.
Funding to Golan Heights
On Monday, Patel revealed details of her meetings in Israel, which included discussions with non-governmental organisations and businesses.
She said they were arranged by Lord Stuart Polak, honorary president of the lobbying group Conservative Friends of Israel.
But it emerged late Tuesday there had been another two unauthorised meetings in September, with Israel's Public Security Minister Gilad Erdan in London and senior foreign ministry official Yuval Rotem in New York.
"I don't understand what more she needs to do to be sacked," one unnamed minister told The Daily Telegraph newspaper.
During her meetings, Patel discussed the possibility of British aid being used to support medical assistance for Syrian refugees arriving in the Israeli-occupied Golan Heights, Downing Street said.
However, reports suggest that she did not explain to May that this involved supplying funding to the Israeli army, which has facilitated the treatment of more than 3,100 wounded refugees in Israeli hospitals since 2013.
Britain views the Golan Heights as occupied territory and a minister told MPs on Tuesday that funding the Israeli Defence Forces there was "not appropriate".
A senior Palestinian official on Wednesday condemned the meetings as "scandalous", urging May to take action.
"I think it is scandalous and that leads me to question how many more cases, not just in Britain but other places, have not been exposed," Hanan Ashrawi told AFP.
In a further development on Wednesday, Israel's Haaretz newspaper reported that Patel visited a military field hospital in the Golan Heights as a guest of the government.
Patel's ministry declined to comment on the report.
Breach of ministerial code
Patel was a leading campaigner for Britain to leave the EU in last year's referendum, and is a prominent figure in May's cabinet.
The daughter of Ugandan Indians, the 45-year-old has been an MP since 2010, and is widely believed to have ambitions on Downing Street.
On Monday, she apologised that her "enthusiasm to engage in this way could be misread, and how meetings were set up and reported in a way which did not accord with the usual procedures".
But the main opposition Labour Party has demanded an investigation into whether her behaviour breached the ministerial code.
Labour MP Yvette Cooper, who chairs the home affairs select committee, said the affair exposed the government's weakness.
"There is no sense of direction, no sense of grip in any of these controversies," she told BBC television.
"This is really damaging for the whole country, not just the Conservative Party."