The Reagan administration wants to get the federal government out of the riot- and crime-insurance business, saying that it is confident that private industry can handle the demand now that urban violence is abating.

The administration also has become concerned because the 14-year-old programs, which have never cost the taxpayers money, have been forced to dip into their $250 million borrowing authority.

Unless Congress votes to extend the programs they will die Sept. 30.

"We have not asked Congress to continue the program, and right now we do not expect them to," said Robert J. DeHenzel, director of the urban property insurance program of the Federal Emergency Management Agency. "There was a need," he said, "and now it's passed."

DeHenzel spoke, however, before a Senate subcommittee unexpectedly approved an amendment yesterday to extend the program for two years. A House subcommittee previously had done the same.

The federal government started the programs after the urban riots of the late 1960s to cover urban residences and businesses that individual insurance companies would not insure because of the potential for violence. The District, Maryland and Virginia are among the 28 jurisdictions in the riot-reinsurance program and the 30 in the crime-reinsurance program.

Following federal guidelines, states were enabled to set up FAIR (fair access to insurance requirements) programs in which consortiums of private insurance companies shared the burden of paying claims. The companies paid some of the money directly, but most of the cost of the claims was covered by "reinsurance" premiums the companies pay the government.

But because crime-insurance claims have outdistanced riot-related claims, program managers have begun using the premiums from one program to pay for claims in the other. Last August both funds ran out of money, giving FEMA a new reason to recommend that the programs be terminated.

To make up the shortfall, FEMA increased premiums 10-fold, but that caused too many policyholders to drop out. As a result FEMA has been forced to use $19 million of its $250 million borrowing authority for the first time, and expects borrowing to hit $40 million by Sept. 30.

Edward T. Pasterick, assistant administrator for insurance operations at FEMA, said, "Industry participation has increased to such an extent that the federal program is superfluous."

However, a report that FEMA sent Congress last month said, "There is evidence that some insured would experience difficulty in being placed in the private market."

In the Washington area 7,283 homeowners and 3,432 firms have federal riot insurance. In addition, 120 homeowners and 287 businesses in the District have federal crime-insurance policies.(FEMA has no other figures available on crime-insurance policies in the metropolitan area.)

These policyholders are not expected to see any difference if the federal government drops out, according to Pasterick; the insurance groups are simply expected to turn to other companies for reinsurance.