Amber Rud left the cabinet and handed it to the Conservative Whip, saying it couldn't be "until the" moderate conservatives "were expelled.
The Secretary of Labor and Pensions said she no longer believed that leaving the EU with an agreement was "the government's primary objective."
Ms Rudd described the dismissal of 21
No. 10 stated that he was" disappointed "by the resignation of a" talented "minister.  But a spokesman added that "all ministers who joined the cabinet signed up to leave the EU on October 31, coming what they can."
A senior government source said "resignations to pursue headlines would not change the fact that people want Brexit to be made so that the government can meet its internal priorities. "
Labor stated that Ms. Rudd's resignation indicates that the government is" falling apart. "
The Hastings and Rye MP, who supported the referendum in 2016, said her resignation was a "difficult decision".
"I will consider my position – whether I will run for an independent conservative if elections are to come," she told the Sunday Times.
In her resignation letter to Prime Minister Boris Johnson, she said: "I joined your cabinet in good faith: you agreed that No Deal should be on the table because it was the means by which we would have the best chance reaching a new deal that we have to leave on October 31st.
"However, I no longer believe that leaving the bargain is the government's primary objective."
In an interview with the BBC in January, Ms Rudd pledged to avoid Brexit without the bargain she defined it as "the worst possible outcome".
Earlier this week, Mr Johnson removed the whip of 21 Tory MPs – including two former chancellors – after they voted to control opposition MPs over Commons and begin the process of blocking the fruitless Brexit.
Ms Rud described the expulsions as a "short-sighted rejection" of "widely-regarded and dedicated Conservative MPs".
"I cannot support this political act of vandalism," she added.
One of the rebel MPs David Gauke, tweeted that Ms Rud had been "extremely brave" and her concerns "reflected the views of many of my (former) colleagues".
"In one way or another, it's time for them to act," he added.
Rebel colleague Rory Stewart described Ms Rudd as "a true conservative of one nation" adding: "we must unite to support the Brexit deal and get it done."
Health Minister Matt Hancock said the Conservative Party "had always been a broad church" and he was "gutted" to see Ms. Rudd leave.
In response to Ms Rudd's resignation, Brexit secretary in the shadow of Sir Keir Starmer tweeted that Mr Johnson's government was 'falling apart'.
Labor Party chairman Ian Lavery said the resignation was a sign that "nobody trusted" Mr Johnson.
"The prime minister has run out of power in record time and his plan for Brexit is exposed as shame," he said.
SNP Westminster leader Ian Blackford called on the prime minister to resign, arguing that he had "no support or reliability left."
"The Tory Boris Johnson government is on the verge of collapse – without a majority, without a mandate, and with the right to pursue its reckless plans to impose an ultimate Brexit," he said.
Who is Amber Rud?
- The 56-year-old has been a Hastings and Rye MP in East Sussex since 2010.
- Her majority in the 2017 election was only 346 votes.
- In the 2016 referendum, she was a stickler for her brother. helped her fund the campaign
- Ms Rud was appointed Secretary-General in July 2016
- She resigned as Home Secretary in 2018 because of the scandal with Winder, saying she "inadvertently misled" MPs
- ] But the inquiry concluded that she had been released by her staff and was returning to the cabin as Secretary of Labor and Pensions months later
- Ms Rud was married for five years to the late journalist and writer AA Gil
- A graduate of the University of Edinburgh, having previously worked in banking case and recruitment
- She has been credited as a hit film consultant since 1994. Four Weddings and a Funeral