"While my actions were meant with the best of intentions, my actions also fell below the standards of transparency and openness that I have promoted and advocated", Patel wrote in the letter to May.
British secretary of state for global development Priti Patel has apologised for holding several secret meetings with Israeli officials during a family holiday in August, in which she discussed a number of issues, including India.
It also emerged that Patel met Israeli public security minister Gilad Erdan in the British Parliament on September 7, and foreign ministry official Yuval Rotem in NY on September 18.
Ms Patel's downfall came after it emerged she had a series of 12 meetings with senior Israeli figures during a holiday in the country in August.
Priti Patel wanted to send British aid money to support an Israeli army programme treating wounded Syrian jihadists, including al-Qaeda fighters, in the occupied Golan Heights.
Patel also said: "This summer I travelled to Israel, on a family holiday paid for by myself".
After a hastily arranged meeting not long after Patel landed in London, May's office released her minister's letter of resignation, in which Patel said her conduct in Israel had fallen "below the high standards" required of her post.
Patel apologized, but when details of two further meetings emerged, May acted.
No 10 on Tuesday said Patel had not informed the prime minister about the "aid to Israel" discussions at a crunch meeting on Monday which was supposed to draw a line under the row.
Britain's worldwide development secretary Priti Patel leaves 10 Downing Street in London, Wednesday, Nov. 8, 2017.
"But that must be done formally, and through official channels".
A spokesperson for May's office said on Monday: "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".
Patel then met an Israeli foreign office minister in NY on September 18.
The imminent sacking of cabinet minister Priti Patel took another turn this morning when a journalist revealed Theresa May's office did know about her meetings in Israel.
She was accompanied at all the meetings bar one in Israel by the honorary president of the Conservative Friends of Israel lobbying group, Lord Polak.
The ministerial code that governs the behavior of members of the British government makes no specific mention of secret meetings with foreign heads of government, but it does urge ministers to take "special care" when talking about issues "which are the responsibility of other ministers".
Number 10 confirmed that Patel had discussed the possibility of United Kingdom aid being used to support medical assistance for refugees from the Syrian civil war arriving in the Israeli-occupied Golan Heights.
Ms Patel is given a face-to-face reprimand by the Prime Minister and reminded about her "responsibilities under the ministerial code".