Labour's shadow cabinet office minister Jon Trickett said there had been a "clear breach" of the ministerial code, while shadow global development secretary Kate Osamor called for an investigation, describing Patel's apology as "a desperate last-ditch attempt.to save her job".
Worldwide development secretary Priti Patel has admitted foreign secretary Boris Johnson did not know about her trip to Israel until she was there - and revealed a slew of meetings not previously disclosed.
Opposition parties had called for Patel, the senior-most Indian-origin member of May's Cabinet, to resign as minister in charge of the Department for International Development (DfID) and the country's aid budget if it emerges that she breached the ministerial code of conduct.
"The Foreign and Commonwealth Office was aware of my visit while it was under way".
Patel also said: "This summer I travelled to Israel, on a family holiday paid for by myself".
Kate Osamor, the shadow global development secretary, told the Commons on Tuesday that it was "hard to think of a more black and white case of breaking the ministerial code of conduct".
Prime Minister Theresa May has directed the UK Cabinet Office to look at how the country's ministerial code of conduct can be tightened in the wake of one of her minister's meetings in Israel not being disclosed through the usual channels. While away, I had the opportunity to meet a number of people and organizations. "There is no United Kingdom financial support for the Israeli army", a Downing Street spokesperson said after it emerged that in the wake of her visit in August, Patel had discussed potentially providing some of Britain's aid money to Israel's armed forces which run field hospitals in the Golan Heights area.
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The list showed that Patel also held meetings with Yuval Rotem, a senior official at the Israeli foreign ministry; Gilad Erdan, the minister for public security, information and strategic affairs; and Yair Lapid, a former finance minister in Netanyahu's coalition government and the leader of Israel's centrist Yesh Atid party.
"I am sorry for this and I apologise for it", Ms. Patel said in a statement.
"The prime minister met the secretary of state this morning to remind her of the obligations which exist under the ministerial code".
The Netanyahu meeting included "prospects for closer collaboration between Israel and the United Kingdom on development and humanitarian issues", Israel-based newspaper Haaretz reports, noting that no minutes were kept.
Downing Street officials are already furious with Ms Patel, who has also admitted misleading journalists about the Israel trip.
The Secretary of State said she had seen for herself the work of Jewish charities in Israel, and said she was "struck by the achievements of the state of Israel".