The House, after two days of debate, yesterday approved a housing authorization bill of more than $16 billion that Republicans said will almost certainly be vetoed by President Reagan.

The measure, passed 285 to 120, exceeds the administration request for housing programs in the next fiscal year by about $5 billion. The authorized funds include $5.9 billion for low-income housing assistance, $2 billion for public-housing modernization and construction and $3.4 billion for rural housing programs.

The bill also would extend permanently Federal Housing Administration (FHA) mortgage-insurance programs and reauthorize the Urban Development Action Grant (UDAG) program, which the administration has been trying for years to kill.

Rep. Chalmers P. Wylie (Ohio), ranking Republican on the House Banking, Finance and Urban Affairs Committee, said an "almost certain veto" awaits the bill in its present form.

He quoted Office of Management and Budget Director James C. Miller III as describing the legislation as a "costly and burdensome measure and one I am confident will be vetoed . . . . "

Major new housing-authorization legislation has not cleared Congress since Reagan took office in 1981. Instead, existing housing laws have been extended annually.

Last year, the House approved a new housing bill, but it was bottled up in the Republican-controlled Senate. In March, however, the newly Democratic Senate passed its version of a $15.6 billion housing bill.

Yesterday's action moved Congress one step closer to final enactment of a new housing measure and a likely veto confrontation.

During the debate, the House reversed a position it took last year and delivered a setback to Rep. Jack Kemp (R-N.Y.), an announced contender for the 1988 Republican presidential nomination.

Last year, Kemp persuaded his colleagues to adopt a concept he calls "urban homesteading" as part of the ill-fated housing legislation. Under his proposal, low-income public-housing tenants could buy their housing units for a maximum of 25 percent of market value and be eligible for low-interest mortgages.

Offering his plan as an amendment to this year's housing bill, Kemp called it "a radical solution" to housing problems and "a piece of America's dream that we ought to offer to the inner-city poor."

But Democrats, led by Reps. Henry B. Gonzalez (Tex.) and Bruce A. Morrison (Conn.), assailed Kemp's plan as "a cruel hoax and a raid on the Treasury." They said, because the proposal would not restrict resales of public-housing units after five years, real-estate speculators are likely to use the program to gain control of the most desirable public-housing facilities.

The House effectively killed the Kemp plan, 258 to 161, Wednesday. With Kemp away on a campaign trip, Wylie yesterday sought to revive it but lost, 243 to 162.