The Senate, responding to what supporters said was a "nationwide call for effective action," gave final approval yesterday to a bill providing $923 million over the next two years to help homeless people.

The House is expected to take final action early in the week, sending the measure to an uncertain fate at the White House, where a spokesman said, "There are problems with the bill, but we have to take a look" at the final version when it arrives.

The homeless-aid bill passed the Senate 65 to 8 during an infrequent session yesterday called to continue debate on the huge trade bill.

The final bill emerged after six weeks of negotiations by a House-Senate conference committee ironing out differences between the bills for the homeless passed by each chamber.

A Senate housing subcommittee spokesman said the measure gives governors and mayors primary responsibility for developing methods to help homeless people and authorizes federal funds for programs.

The bill authorizes $443 million this fiscal year to aid the homeless and another $480 million in fiscal 1988, according to a subcommittee aide. More than half of those funds are for housing programs and support services.

It provides $220 million over the next two years for emergency shelter grants to states, which distribute the money through nonprofit agencies. Much of that money will be used to turn old buildings into shelters.

Other provisions of the bill would authorize funds for programs to improve the physical and mental health, education and nutrition of the homeless. The measure includes a program for a national competition for funding among nonprofit agencies to create programs to help the homeless move out of shelters into their own housing.