Republicans claimed significant gains in the nation's state legislatures yesterday after conducting a $3 million campaign to build up their muscle for the reapportionment fights coming up.

At Republican national headquarters here, officials calculated that the GOP had picked up control of five new legislative chambers and gained a tie in at least one other.

Even more importantly, said Joe Gaylord, who heads the Republican National Committee's local election unit, the party now has effecitve veto power or leverage in the redistricting process in 32 states. Republicans control at least one house or the governor's office in those states, Gaylord said.

"It's significant for the health of the Republican Party for the next decade," said William Pound, director of state services at the Denver-based National Conference of State Legislatures. "It will institutionalize their mandate . . . they can use this to build a Republican foundation."

Others were more skeptical about the import of Tuesday's state legislative results.

"Considering the supposed sweep of the Republican Party, I don't think that's much," one Council of State Governments official said of the GOP projections.

Going into yesterday's elections, the Democrats controlled both houses in 29 states, according to the council's figures. The Republicans had 13 states (not counting Nebraska's unicameral, nonpartisn legislature). The parties had split control in seven states.

If the RNC projections from Tuesday's balloting hold up, the Democrats will retain control of both houses in 26 states. The Republicans will control 15 states and the two parties will control one house each in eight states.

There were some 5,000 state House or Senate seats up for grabs Tuesday in a total of 43 states.

Although returns are still incomplete in many instances, Gaylord estimated that the GOP had registered a net gain of 212 seats -- far more than than the 51 the Republicans picked up in the Nixon landslide of 1972.

Pound was more cautious, projecting a net gain of 170 seats for the Republicans thus far but acknowledging that the final number could be higher.

"It's a giant chess board," he said. "Pieces are still moving everywhere."

RNC officials said they were fairly certain they had won control in the Ohio Senate, the Illinois House, the Montana House, and the Washington state House and Senate.

In addition, Gaylord said, the GOP gained a tie in the Pennsylvania Senate -- where the deciding vote in organizational matters will be cast by a Repulblican lieutenant governor.

Pound said his figures showed the Republicans also gained a tie in the Alaska Senate. But he said it was too soon to give the Washington state Senate to the GOP.

"It's a continuation of a trend which began two years ago," Pound said. "The Republicans didn't gain as much this time . . . but we've been very aware of the conservative trend in state legislatures. . . . Conservatives that were elected yesterday will be the ones that redraw the district lines for the U.S. House [based on the 1980 census]. Those districts will stand for the next 10 years."

Legislative districts are supposed to reflect the one-man, one-vote rule, but the boundary lines still can be gerry-mandered with all sorts of patisan twists and turns.

GOP National Chairman Bill Brock began the drive to cut into Democratic domination of state legislatures with a $2 million commitment in 1978 and then followed up for 1980 with a $3 million effort, financing selected candidates across the country.

Brock has calculated that the last redistricting in 1971 -- when the Democrats controlled 23 legislatures to 16 for the Republicans -- cost the GOP about 40 seats in Congress. The Republicans are still below that level. Even so, however, they are much better off than they were before the 1978 elections, when they effectively controlled both houses in only four states.