The government led by his predecessor, former Prime Minister Keir Starmer, announced last year it supported Heathrow's expansion proposal, which must undergo a lengthy planning process before construction can begin.
"I think, principally, it's a matter for London," Burnham told the BBC in an interview at the start of the governing Labour Party's annual conference.
"I think you've got to hear the voice of people there first. It's not right for me to just jump straight in on the back of the consultation."
Burnham's refusal to immediately back the plan is the latest development in a long-running debate over a project that has divided politicians for two decades.
Heathrow said at the weekend that plans to open the third runway could be delayed by four years, meaning it would not be operational until 2039.
The airport operates at 99% capacity and risks being overtaken in Europe by other airports. Its two runways compare with four each in Paris' Charles de Gaulle and Frankfurt Airport, and six at Amsterdam's Schiphol.
Heathrow is just 15 miles (24 km) west of London. Residents have for decades complained about noise pollution, safety risks from flights over the densely populated city, and more recently, about the impact of soaring carbon emissions.
But businesses and workers' unions have raised concern about delays to Heathrow's expansion and the impact on Britain's growth prospects and jobs.
GMB, a union which represents workers across Heathrow, said while local voices should be heard, many were workers who supported expansion and that "this isn't just a matter for London".
"Heathrow is Britain's front door, and businesses in every region trade through it," said Warren Kenny, GMB London Regional Secretary. "I urge the prime minister to unleash our potential and build."
(Reporting by Andrew MacAskill and Alistair Smout, editing by Elizabeth Piper)

British Prime Minister Andy Burnham attends a bilateral meeting with Norway's Prime Minister Jonas Gahr Store on the opening day of the Labour Party annual conference in Liverpool, Britian, 27 September 2026. The conference runs until 30 September. EPA/CHRIS RATCLIFFE / POOL
Comments
Scroll down to load comments...