Priti Patel has resigned as UK international development secretary amid controversy over her meetings with Israeli officials.
She was ordered back from an official trip in Africa by the PM and summoned to Downing Street over the row.
In her resignation, Ms Patel apologised and said her actions “fell below the standards of transparency and openness that I have promoted and advocated”.
The PM said her decision was “right” as “further details have come to light”.
Ms Patel had apologised to Mrs May on Monday after unauthorised meetings with Israeli politicians in August came to light, but it later emerged she had two further meetings without government officials present in September.
Ms Patel had a 30 minute meeting with Mrs May, arriving at 10 Downing Street via the back door after returning to the UK.
Her resignation from the cabinet is the second in seven days, after Sir Michael Fallon quit as defence secretary on Wednesday last week amid allegations about his behaviour.
In her letter to Theresa May, Ms Patel said: “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.
“I offer a fulsome apology to you and to the government for what has happened and offer my resignation.”
In her reply, Mrs May said: “Now that further details have come to light, it is right that you have decided to resign and adhere to the high standards of transparency and openness that you have advocated.”
She added that Ms Patel should “take pride” in what had been achieved during her time as secretary of state.
The BBC’s chief political correspondent Vicki Young said Theresa May “decided to give her colleague the dignity of resigning”.
But she said the response from Mrs May was “interesting”, saying: “It was clear from Theresa May that if she hadn’t resigned, she would have been sacked.”
Who is Priti Patel?
Elected as Conservative MP for Witham in May 2010
Served as a Treasury minister from July 2014 to May 2015
She then became employment minister from May 2015 to July 2016
Appointed International Development Secretary in July 2016
A longstanding Eurosceptic, she was a leading figure in the Vote Leave campaign during the EU referendum
Ms Patel was formally reprimanded in Downing Street on Monday, where she was asked to give details about a dozen meetings she had with Israeli officials while on holiday, which were not sanctioned by the Foreign Office.
The MP said she had been wrong to suggest to the Guardian that Foreign Secretary Boris Johnson knew of the trip in advance when he had only learnt about it while it was under way.
Then, details of two other meetings emerged. Ms Patel met Israeli public security minister Gilad Erdan in Westminster on 7 September.
And on 18 September she met foreign ministry official Yuval Rotem in New York.
It is not yet clear whether or when Ms Patel had informed the prime minister about these meetings or of her plans to look into giving tax-payers’ money to the Israeli military to treat wounded Syrian refugees in the Israeli-occupied Golan Heights region – a request that was turned down as “inappropriate” by officials.
In her letter to Ms Patel, the prime minister wrote: ”As you know the UK and Israel are close allies, and it is right that we should work closely together. But that must be done formally, and through official channels.
”That is why, when we met on Monday I was glad to accept your apology and welcomed your clarification about your trip to Israel over the summer. Now that further details have come to light it is right you have decided to resign.”