A bipartisan Senate, with the backing of the White House, on Tuesday easily agreed to a landmark bill to strengthen the nation's fair housing laws and to bar discrimination against the handicapped or families.

In a message to the Senate, President Reagan called the fair housing bill a "landmark civil rights bill" and urged it be sent to the White House quickly.Sen. Edward Kennedy, chairman of the Judiciary Committee, and civil rights supporters called it the most significant improvement in civil rights law in 20 years and said it will finally put teeth into federal fair housing rules.

"The existing fair housing law is a toothless tiger. It recognizes a fundamental right but it fails to provide a meaningful remedy," the Massachusetts Democrat said.

The bill passed the Senate on a 94-3 vote. It had passed the House in June and a final, compromise version will be soon worked out and sent to Reagan to sign.

For the first time, the federal government will be allowed to investigate and prosecute housing discrimination on the basis of race, sex, national origin, color, religion, handicap or the fact that the family has children under age 18.

The original fair housing law of 1968 made discrimination by landlords or home sellers illegal but did not give the Department of Housing and Urban Development enforcement power.

Recent HUD studies had shown that an estimated 2 million instances of housing discrimination on racial grounds occur each year. A black person who visits four agents can expect to encounter at least one case of discrimination 72 percent of the time for rentals and 48 percent of the time for sales, according to one HUD study.

Under the bill, new housing with more than four apartments will be required to be accessible to the handicapped. Doors, bathrooms and kitchens must be constructed to allow access for wheelchairs. Light switches and thermostats must be low enough for wheelchair-bound tenants.

No apartment or housing complex may exclude families with children under 18 or evict pregnant women. But those housing projects constructed for the elderly may continue to exclude families.

Only three Republicans, Jesse Helms of North Carolina, Gordon Humphrey of New Hampshire and Steven Symms of Idaho, voted against it.

Humphrey had argued that it would raise construction costs although it has the support of associations representing Realtors, home builders and architects.