UK Coal is consulting on plans to shut Kellingley in North Yorkshire, which employs 700 people, and Thoresby in Nottinghamshire, which employs 600.
It will leave employee-owned Hatfield colliery in South Yorkshire as Britain's last remaining deep-pit mine.
Jobs are also likely to go at UK Coal's head office in Doncaster.
It will mean the majority of the 2000 people employed by UK Coal - which also operates six surface sites - facing a bleak future, nine months after it was rescued from administration.
The firm is hoping to secure an emergency cash injection of up to £20 million through a combination of funding from the Government and the private sector but will still need to make the cutbacks even if it succeeds.
A spokesman said: "We have started consultations with the unions on looking at the way forward - that is, looking at reducing numbers in the coming months.
"We are looking to secure the best outcome possible."
Asked if he was ready to act to "keep these mines alive", Mr Cameron told BBC1's Breakfast: "Yes, we will do everything we can. We are talking to the company, we are talking to other businesses related to this company.
He added: "There are obviously limits but we will work with them as closely as we can."