Rhodesia's whites today overwhelmingly approved a new constitution that is scheduled to bring a form of qualified black majority rule to this war-torn country and end almost nine decades of white rule.

Their endorsement of the constitution paves the way for its acceptance by Rhodesia's white Parliament, which now ruled under a constitution drawn up when the former colony broke away from Britain in 1965. Universal suffrage elections for a biracial government are set to follow in April.

That government would, however, be under constitutional restraints guaranteeing the whites, who make up 4 percent of Rhodesia's 6.7 million population, a considerable voice in the politics of the new state, which would be called "Rhodesia-Zimbabwe." The name is hyphenated compromise between white and black names for the country.

By a majority of 85 percent, the whites today gave Prime Minister Ian Smith their official backing for the agreement he entered into last March 3 with three moderate black leaders, Bishop Abel Muzorewa, the Rev. Ndabaningi Sithole and Chief Jeremiah Chirau.

About half of the country's 94,700 registered white voters cast ballots. There are 230,000 whites in Rhodesia.

Visiting the returns center at Salisbury's central post office tonight, Smith said he hoped the vote would be taken "as an indication of [Rhodesians"] integrity and good faith in what we're trying to do." The white leader said he hoped there would now be some "reciprocity" on the part of the "leaders of the free world."

But even with this open white support, Smith and his three black colleagues will continue to face stiff military opposition to their plans from the Soviet-supported guerrilla armies of the two black Rhodesian leaders who have opposed the settlement.

The conflict between government forces and those of Joshua Nkomo and Robert Mugabe, who together form the Patriotic Front, is causing at least 100 deaths a week and has put at least 80 percent of the country under martial law.

Some observers labeled today's election "irrelevant," claiming that the transition to black majority rule is now irreversible. Others feared the whole effort may be overtaken by the worsening war.

More than 18,000 white Rhodesians didn't wait for today's constitutional referendum. They left Rhodesia during 1978, setting a record emigration rate for the troubled country.

Smith, looking pale and gray, but relaxed, set an example today by casting his vote in the community hall of his comfortable neighborhood, salisbury North.

Asked later how he voted, Smith, in his evasive way, replied. "I voted with a cool head and used my judgment in the interest of Rhodesia, and voted the right way."

Before the election, Smith stumped vigorously to garner today's "yes" vote. Reiterating what he has said before, he told his white electorate that the constitution was the best they could hope for.

"I don't promise you utopia," he said, explaining openly, however, that the blacks' power would be limited by certain clauses of the constitution that "for the first five years will provide stability during the crucial initial years of majority rule. As will be seen in the constitution, effective white influence during this period will be considerable."

Under the new constitution the whites will be given a certain number posts in the Cabinet and will be assured of 28 seats in the 100-member Parliament. They will also have a veto over any legislative changes in the military, police, civil service and judiciary.

Despite a widely publicized effort by right-wing whites who oppose black rule and by liberal whites who believe that without the participation of the guerrilla chiefs, the biracial experiment of Smith and his three black partners is bound to fail, only 15 percent voted "no" to the new constitution.

Today's referendum was the fulfillment of a promise Smith gave the whites during the last general election in August 1977, when he said he would allow them to voice their opinion of any settlement he worked out with black leaders.

[Reuter reported from London that British officials said Secretary of State Cyrus Vance and British Foreign Secretary David Owen will meet in Washington Friday and Saturday to discuss the next possible steps towards a negotiated settlement in Rhodesia.]