Labour must do all it can to avoid a “psychodrama” over Andy Burnham’s possible return to parliament, Shabana Mahmood, the home secretary, has said.

Mahmood is chair of Labour’s national executive committee (NEC), which was due to meet later on Sunday to decide whether Burnham should be allowed to seek selection for the Gorton and Denton byelection, which would involve him giving up his Greater Manchester mayoralty.

Speaking to Sky News, Mahmood said her role as chair meant she could not comment on whether it was a good idea for Burnham to seek to return as an MP, widely seen as a route for him to challenge Keir Starmer as prime minister.

But she said voters would not tolerate a long period of turmoil and internal struggle from the government, as happened under the Conservatives, who cycled through five prime ministers in six years.

“Everyone has to make their own decisions. What I would say is, I think everybody could do with less psychodrama,” Mahmood said. “And my clear message to all of my colleagues, whether they are in cabinet, or elsewhere in the country, is: we get to decide if we indulge in a psychodrama.

“The country was absolutely fed up to the back teeth of the Tories and all of their psychodramas, the constant arguing. So my clear message to all colleagues everywhere is, just calm down. We’re in government. Labour governments don’t come along that often in the history of our great country. We have the absolute privilege of being the government of our country. We should all pull together and make a success of it.”

She praised Burnham, indicating she felt he could add to the party in parliament. “He’s an exceptional politician, and of course I always think we should have all of our best players making their contribution to the Labour government,” she said.

The Greater Manchester mayor said on Saturday afternoon he wanted to contest the seat after the sitting MP, Andrew Gwynne, said he intended to stand down.

Burnham’s allies – including ministers, MPs and trade union leaders – say that as one of the country’s most high-profile and popular Labour politicians, he must be allowed to fight the seat and attempt a return to parliament. But with Burnham having made no secret about his leadership ambitions, those close to the prime minister were on Friday night urging him to take steps to prevent him standing.

Sunday’s NEC meeting, Mahmood confirmed, would simply be to decide whether Burnham would be allowed by the party to give up his mayoral post, thus triggering an expensive mayoral byelection, if he stood for the seat and was selected.

Speaking later on BBC One, Mahmood said the meeting would not be of the full NEC, which has 40-plus members, but of a smaller “officers’ group”, believed to comprise about 10 people. For such selection choices, she said, the use of the smaller group was “very normal practice”.

If the meeting did allow Burnham to proceed, the NEC could subsequently make other decisions such as imposing an all-female shortlist, Mahmood said. “Today, we will be deciding one question, which is: Andy, as a metro mayor at the moment, has sought permission to stand in the byelection,” she said. After this there would be a shortlisting process for the candidacy, she went on, adding: “There will no doubt be a discussion about whether we want to have an all woman shortlist at some point.”

Asked about whether Burnham as an MP could seek to challenge Starmer, Mahmood told the BBC she would trust him when he said he hoped to go into parliament to support Starmer. “Andy has said, in his own words, that Keir is the best person to be the prime minister, and has made it very clear in his letter what his motivation is for wanting to come into parliament,” she said.

“I do believe Andy Burnham, because I take him at his word. I’ve never had any reason not to take him at his word. I trust him, as I say, we work very closely together, and I am going to take what he says at face value, because I know I can do that with Andy.”