A Defense Department official, sharply increasing previous estimates, said yesterday that it may cost $5 billion to $10 billion to clean up hazardous waste at active and closed military installations.

Last year the Pentagon estimated the cleanup costs at $1.6 billion; last month it raised the estimate to $3.2 billion.

Carl Schafer, director of environmental policy at the Defense Department, told the House Appropriations military construction subcommittee that the estimate is rising as the department learns about the extent of the problem and how to correct it.

The Pentagon, which may have 800 or more sites to purge of toxic waste from weapons production and military operations, is not covered by the "Superfund" cleanup program operated by the Environmental Protection Agency.

Unlike the Superfund, which gets most of its money from a special tax on chemicals and petroleum, money for the military cleanup program comes from general tax revenues.

The Defense Department, which is spending $314 million on toxic waste cleanup in the current fiscal year, proposes to spend $321 million in fiscal 1986. Most of the money is devoted to assessing the the problem and to pre-cleanup studies.

Schafer said the Pentagon is committed to cleaning up all its toxic waste sites, including 33 on the EPA's list of locations requiring priority attention. He said the Defense Department is coordinating its activities with the EPA.

But Rep. Vic Fazio (D-Calif.) said he believes the EPA should be given a direct "oversight role . . . . Cooperation alone is not enough."