Andy Burnham has signalled his support for dedicated options at the next census to allow people to define themselves as black English or Asian English.
It comes after Liberal Democrat MP Josh Babarinde called for legislation to widen ethnicity options for respondents at the next population count, due in 2031.
The last census, held in 2021, saw English offered within a broader white category, but without specific options for black English or Asian English.
Asked at Prime Minister's Questions whether he would support Babarinde's proposal, Burnham said he had not seen details of the plan.
But he added: "I stand here thinking that I would want to support that bill, to directly take on the poisonous politics we've seen from some in this House".
"We must bring people back together. I am interested in working with anyone in this House who shares that aim," he added.
Burnham did not respond to a follow-up question from Lib Dem leader Sir Ed Davey about whether he would meet Babarinde to discuss his plan, and he did not specify whether the government would give it time for debate in Parliament.
Babarinde introduced his proposal for legislation on Tuesday, under a rule that allows MPs to propose new laws in a 10-minute speech.
