Priti Patel has apologised for holding a series of undisclosed meetings with senior Israeli officials during a private holiday over the summer.
The international development secretary met Prime Minister Benjamin Netanyahu and other senior figures without "following the usual procedures".
Ms Patel apologised for not informing the Foreign Office and suggesting Boris Johnson knew in advance of the visit.
Labour said the "shocking" admission warranted a Cabinet Office inquiry.
Downing Street said it welcomed Ms Patel's "clarification" and that at a meeting with Theresa May earlier, the prime minister had "reminded her of the obligations which exist under the ministerial code".
No 10 said it had not been aware of Ms Patel's meeting with Mr Netanyahu until Friday but insisted that Mrs May still had confidence in the minister.
The BBC's diplomatic correspondent James Landale said there were clear rules about what ministers could and could not do and "in normal circumstances" Ms Patel would be in "serious trouble".
But he said the fragility of Mrs May's government and the fact that the PM would not want to lose another cabinet minister after Sir Michael Fallon's recent resignation could help her.
The BBC revealed on Friday that Ms Patel held a number of undisclosed meetings with business and political figures during a family holiday in August, including Yair Lapid, the leader of Israel's centrist Yesh Atid party and Jean Judes, executive director of disability charity BIS.
No diplomats were present at the meetings, at which the minister was accompanied by an influential pro-Israeli Conservative peer and campaigner Lord Polak.
Ms Patel, who is a long-standing supporter of Israel and a former vice-chairman of Conservative Friends of Israel defended her actions, saying she had paid for the holiday herself and while in Israel had taken the opportunity to meet "people and organisations" for the purpose of building links between the two countries.
She also told the Guardian that "Boris [Johnson] knew about the visit, the point is that the Foreign Office did know about this".
Suggesting that the reaction to her visit had been "extraordinary", she added that it was "for the Foreign Office to go away and explain themselves".
But in a statement "clarifying her position", Ms Patel said she had in fact attended 12 meetings, not just the handful previously reported, and that her earlier comments may have "implied" otherwise.
Among meetings that were not previously reported, she said that she had met Mr Netanyahu to discuss his forthcoming visit to the UK as well as the Israeli "domestic political scene" and UK-Israeli collaboration.
She said she had also met other senior figures in the Israeli government, including security minister Gilad Erdan and foreign ministry official Yuval Rotem.
Ms Patel has also set the record straight about when the government was informed about the trip.
While the Foreign Office was aware of the visit "while it was under way", she said she was wrong to have given the impression that the department and Mr Johnson knew about it in advance.
She said she "regretted the lack of precision in the wording" of her previous statement about the trip.
"This summer I travelled to Israel, on a family holiday paid for myself," she said in a statement.
"While away I had the opportunity to meet a number of people and organisations...In hindsight, I can see how my enthusiasm to engage in this way could be mis-read, and how meetings were set up and reported in a way which did not accord with the usual procedures. I am sorry for this and I apologise for it.
"My first and only aim as the Secretary of State for International Development is to put the interests of British taxpayers and the world's poor at the front of our development work."
In her statement, Ms Patel also said the Foreign Office was clear that the UK's interests were "not damaged or affected" by her actions.
Labour has called for an inquiry into whether Ms Patel broke the ministerial code or the rules on lobbying.
"Not only does it look like she has broken the ministerial code, she has now been caught misleading the British public," shadow international development secretary Kate Osamor said.
"If she does not now resign, then Theresa May must immediately refer the issue to the Cabinet Office for a full investigation."
Downing Street said the ministerial code was "not explicit" in this area and Cabinet Secretary Sir Jeremy Heyward had been asked to see if it could be made clearer.