Downing Street confirmed that the global development secretary had asked officials from her department to look into whether public funds could be used to support the work after holding secret meetings with Israeli figures including Binyamin Netanyahu, the prime minister.
A Downing Street spokesperson said: "It is not true that the Prime Minister knew about the International Development Secretary's meeting with PM Netanyahu before Friday 3rd November".
"I then discovered this morning that Number 10 had been told by Ms Patel about her meeting with Israeli foreign office official Yuval Rotem in NY and had specifically asked her not to include it".
In reply, May said in a letter to her: "Now that further details have come to light, it is right that you have chose to resign".
On Monday, Ms Patel apologised to Ms May on Monday for failing to report that she had met with senior Israeli officials, including Prime Minister Benjamin Netanyahu, during a holiday.
Soon afterward, Patel submitted a letter of resignation, saying her actions had become a "distraction" from the work of her department and the government in general.
The Jewish Chronicle article also states that the Prime Minister spoke with Ms Patel ahead of the UN General Assembly last month where they spoke of the meeting with Mr Netanyahu, and discussed details to give United Kingdom aid to humanitarian projects run by the Israel.
She then held two additional meetings, one in the United Kingdom and one in the USA, following her return from Israel.
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She apologized, but it has since emerged that she also met in September with Israeli public security minister Gilad Erdan and a foreign ministry official.
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.
The International Development Secretary, who is facing mounting criticism, was "in the air" on her way to Africa, Foreign Office Minister Alistair Burt told the Commons, adding that she "did not suddenly contrive" the visit in order to avoid facing MPs.
Patel admitted that after the 13-day visit, she had wanted to give British aid money to the Israeli army in the Golan Heights.
Under British protocol, a cabinet minister would normally organise meetings through the foreign office and be accompanied by officials, and visits with Israelis would typically be balanced with meetings with Palestinians.
But while acting quickly to force Patel to resign, the loss of an enthusiastic Brexit campaigner from her cabinet team of top ministers could mean that May faces greater pressure from lawmakers to pursue a clean break from the EU.
According to the Jewish Chronicle, Downing Street knew about Ms Patel's meeting with Mr Netanyahu in August.
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".