Diane Abbott has said that she intends to “run and win” as Labour’s candidate in the constituency she has represented for 37 years, amid reports that Labour has offered peerages to MPs to stand down.

The veteran Labour MP said she had never been offered a seat in the House of Lords and would not accept one if offered.

Her statement came ahead of a crucial meeting on Tuesday of Labour’s ruling National Executive Committee (NEC), which will decide whether or not to endorse her and other candidates in a number of remaining seats.

“I am the adopted Labour candidate for Hackney North & Stoke Newington. I intend to run and to win as Labour’s candidate,” Abbott said on X, formerly Twitter.

A close friend, Shami Chakrabarti, said earlier on Sunday that Abbott was still considering her future, while the shadow home secretary, Yvette Cooper, denied any offer of a peerage had been made to the long-serving MP to make way for another candidate.

Cooper told Sky News on Sunday: “It’s not the way the system works. There’s a whole process with the independent committee that will vet nominations. There have to be processes in terms of the numbers of nominations designated by the prime minister and so on.”

But a number of leftwing MPs told the Sunday Times that offers had been made for them to give up their seats.

Cooper said that “no party can do that or make that sort of commitment” but in practice party leaders and the prime minister do have that power. While nominations are vetted by an independent committee, it is for political parties to decide who receives them. The committee checks if the nomination is a person of good standing but does not have a veto.

Abbott was widely expected by Labour MPs to announce her retirement and be given a peerage, until a Labour source briefed last week that she would be banned from standing and Abbott said she still intended to fight to be a candidate.

After a row that dominated last week’s election news, the Labour leader, Keir Starmer, said Abbott was free to stand as a Labour candidate.

Lady Chakrabarti, a former shadow attorney general, said her friend had endured a “sometimes sordid week of unauthorised anonymous briefings by overgrown schoolboys in suits with their feet on the table and maybe watching too much West Wing …”

“I hope they remember it’s supposed to be country first, not faction first,” Chakrabarti told BBC One’s Sunday with Laura Kuenssberg.

Labour has announced a flurry of candidates in safe seats who are close allies of Starmer and have been instrumental in overhauling the party since Jeremy Corbyn’s leadership.

They include six members of Labour’s national executive committee, including its chair, James Asser, in West Ham and Beckton, and in North Durham Luke Akehurst, a key organiser in Labour to Win, which organises support to maintain centrist influence in constituencies and in conference votes.

Others who have been key to Starmer’s project have been given candidacies in safe seats, including Josh Simons, the director of Labour Together, the thinktank behind Starmer’s leadership bid, Alex Barros-Curtis, Labour’s head of legal who was key to the expulsion of Corbyn and a number of legal battles with former staff, and the Resolution Foundation’s Torsten Bell in Swansea West.