He had been facing efforts by local activists in the Grantham and Stamford Conservative Association to dump him as the party’s candidate for the next general election.
Boles said he will stay on as MP and continue to take the Conservative whip at Westminster “if it is offered to me on acceptable terms”.
Chief Whip Julian Smith made clear that Boles was a “valued member of the Conservative parliamentary party which I hope will continue to benefit from his ideas and drive”.
But a senior official at Boles’ local association said they had been “betrayed” and called on Boles to take the “honourable course” and quit as an MP.
In a letter to members obtained by the BBC, he said “a division has opened up between me and members of the association executive”, adding: “Many of them are convinced that the Government should take the UK out of the European Union without a deal.
“While I have consistently argued that Brexit must be delivered, and have voted for the Prime Minister’s deal every time she has brought it to the House of Commons, I am certain that crashing out of the EU without a deal would do great harm to the British people and have done everything in my power to prevent it.”
He said he was disappointed the association executive had tried to force his hand on the issue of fighting the next election, adding: “I have concluded that I am not willing to do what would be necessary to restore a reasonable working relationship with a group of people whose values and values are so much at odds with my own.”
Councillor Martin Hill, vice president of the local association, said “Nick has been at odds with the local party and the Prime Minister for some time” and the announcement “does not come as a complete surprise”.
“I understand that it is Boles’ intention to carry on as the MP for Grantham and Stamford until the next general election despite being elected to represent us in Parliament,” he said.
The process of selecting a new candidate would begin on March 28 “or earlier if Boles takes the honourable course and resigns his seat”.
“This is very disappointing for us all as once again we have been betrayed by our parliamentary representative,” he added.
Treasury minister Robert Jenrick said Boles “remains a valued part” of the Conservative parliamentary party “and I will continue to work closely with him as my constituency neighbour and good friend”.