The secretary of state for international development admitted meeting Netanyahu among other senior figures without "following the usual procedures" but claimed it was simply the result of "enthusiasm" to engage.
"This summer I travelled to Israel, on a family holiday paid for myself. While away I had the opportunity to meet a number of people and organisations. The Foreign and Commonwealth Office (FCO) was aware of my visit while it was underway," she said in a statement.
"In hindsight, I can see how my 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. I am sorry for this and I apologise for it," she noted.
Ministers are required to tell the Foreign Office when they are conducting official business overseas, but a BBC report had claimed last week that British diplomats in Israel were not informed about these meetings.
Downing Street had dismissed it as a "private holiday" with nothing to investigate, but Prime Minister Theresa May had a follow up meeting with the minister over the issue his morning.
"The prime minister welcomes the secretary of state's clarification about her trip to Israel and has accepted her apology for her handling of the matter. The prime minister met the secretary of state this morning to remind her of the obligations which exist under the ministerial code," a Downing Street spokesperson said.
Opposition parties had called for Ms Patel to resign if it emerges that she breached the ministerial code of conduct.
Among her 12 meetings, now made public, included an interaction with Yair Lapid, the leader of one of Israel's main political parties (Yesh Atid), and visits to charity organisations.
The senior Conservative MP's meeting with the Israeli Prime Minister including discussions on her "family background" and "her experience growing up in an area of the UK with a thriving Jewish community".
The two leaders also discussed "the Israeli domestic political scene" as well as his "forthcoming visit to the UK" which took place last week.
Priti Patel also discussed "prospects for closer collaboration between Israel and the UK on development and humanitarian issues".
"The FCO (Foreign Office) are clear that UK interests were not damaged or affected by the meetings on this visit," the Department for International Development (DfID) said.