Labour MPs who have doubts about Jeremy Corbyn's leadership should stay off Twitter and raise concerns "behind closed doors", the shadow business secretary has said.

Angela Eagle, the most senior woman in Corbyn's frontbench team, urged critical backbenchers to focus their fire on the Conservative government rather than their own party.

But she refused to rule out running for the Labour leadership herself at some point in the future. Eagle was speaking at a press gallery lunch in Westminster on Thursday.

She was asked by BuzzFeed News if she had any message for dissenting Labour MPs who took to social media to air their grievances.

"I think that we ought to have our discussions about things like that with each other, rather than in public," she said.

"And certainly not on Twitter, because 140 characters is rarely enough for me, let alone anyone else, to have a sophisticated rant, let alone a more nuanced debate.

"I would say it's really important that we try and focus our fire on the Conservative party, which is doing great damage up and down the country in various ways ... and let's have our discussions about the right way to do that behind closed doors."

A number of Labour MPs have tweeted their frustration with Corbyn since he became leader last September.