In the battle to register new voters for this election year, Republicans gained strength in an arc of states from Alaska through California and across the Southwest and South, while Democrats firmed their base in the Midwest and Northeast.

A Washington Post survey of registration figures in 35 states shows that Democrats failed to achieve their original goal of gaining a national advantage over the GOP.

Instead, the Republican Party, which invested $11 million in voter registration, appears at least to have matched Democratic gains and may have exceeded them.

The figures also suggest, but do not prove, that the evangelical, conservative Christian drive to register church members produced sharply increased white registration in the South and significant GOP gains there.

A separate analysis of 30 states by the Committee for the Study of the American Electorate found a number of long-range trends working to the disadvantage of Democrats.

In states where voters register according to party, the percentage of Democrats fell steadily from 43.8 percent in 1972 to 35.2 percent now.

For Republicans, the decline was 24.4 percent to 22.8 percent, but the trend in recent years has been upward for the GOP.

In addition, from 1980 to 1984, Republicans had net registration gains in 10 states while Democrats improved their advantage over the GOP in four states.

Curtis B. Gans, committee director, predicted a reversal of the 20-year decline in presidential election-year turnout, but he said that 95 million to 96 million voters will go to the polls, well short of the Democrats' 100 million goal.

Among the major findings of The Post's survey: In five southern states reporting final figures, there has been a surge of black registration -- 18.2 percent over two years in Louisiana, 37.1 percent in North Carolina, 18 percent in Florida, 14 percent in South Carolina, 29.6 percent in Kentucky -- and almost all of the increase has benefited the Democratic Party.

But the more striking numbers are in a sudden surge of GOP registrations.

Over two years, Republican strength has grown in Louisiana by 56.3 percent, in Florida by 26.4 percent and in North Carolina by 31 percent.

In the racially polarized politics of the South, with two-thirds of the whites expected to vote for President Reagan and as many as 90 percent of blacks for Walter F. Mondale, Reagan appears the decisive winner among the new registrants.

White registration increased by 1,469,885 in the five states reporting final figures compared to a 418,993 increase among blacks. This suggests that Reagan will have at least a 145,000-vote margin over Mondale among these new voters. Democrats have made strong gains in such northeastern and midwestern states as Pennsylvania, New Jersey and Iowa.

Boosted by the registration drive in support of the Philadelphia mayoral campaign of Wilson Goode, Pennsylvania Democrats added 303,241 to the rolls, according to nearly complete figures that exclude three counties, while Republicans added 114,009. In addition, the 10 percent growth rate for Democrats was twice that of the GOP.

Complete figures were not available in New Jersey, but statistics from five counties -- Essex, Bergen, Morris, Sussex and Warren -- showed the Democrats making a net gain of 38,181 votes, or a 10.5 percent increase, while Republicans declined by 3,660, for a net loss of 1.3 percent.

In Iowa, where Reagan and Mondale appear nearly neck and neck, Democrats registered 51,202 new voters compared to 30,486 for the Republicans, and the rate of increase was significantly higher for the Democrats, 9.3 percent compared to 6 percent for the Republicans.

Through much of the rest of the Northeast and Midwest, registration is nonpartisan or final figures were not available.

In New York, however, a late surge of registration prompted by generally pro-Democratic organizations suggests that the Democrats may have increased their margin there.In most of the western states, the GOP is solidifying its base while Democrats are losing ground.

Although the GOP is a minority party in California, about two-thirds the size of the Democratic Party, state figures show that Republicans have outregistered Democrats by 740,111 to 656,489. The California Republicans' growth rate over the past two years is 18.4 percent, compared to 10.7 percent for the Democrats.

Similar patterns of GOP strength have emerged in such other western states as Wyoming, Oklahoma, Nevada and Alaska.

Wyoming Republicans added 8,446 new voters to their rolls, pushing their total to 125,905, while Wyoming Democrats added just nine voters, and have become even more of a minority party at 84,933.

Democrats in Oklahoma have enjoyed nearly a 2-to-1 advantage, but in two major counties from which preliminary figures were available, Tulsa County and Oklahoma County, Republicans registered 70,513 voters for a growth rate of 36.6 percent, while Democrats registered 60,255 for a growth rate of 19.3 percent.

In Nevada, Republican strength has grown by 18.2 percent with 22,602 new voters, while Democrats, still the nominal majority party, increased by 9,729 new voters, or a pickup of 5.6 percent.

Alaska Republicans gained 13,005 new voters, for a 27 percent increase, while Democrats, the majority party, increased by 8,005, or 12.5 percent.

Numerically, Democrats in New Mexico did better than Republicans, registering 33,446 compared to 31,356.

But the New Mexico GOP is half the size of the Democratic Party, and consequently the Republican growth rate was 17.7 percent, nearly double the 9.1 percent growth of the Democratic Party.

The only western state where Democrats significantly outdistanced Republicans is Oregon, where preliminary registration figures through Sept. 1 showed Democratic gains of 35,186, a 5 percent growth rate, while the GOP picked up 10,546 new voters, a 2 percent growth rate. The competitive registration drives in a number of states ended in what amounts to a draw.

Maryland, for example, added 284,652 new voters for an increase of 14.4 percent over two years, but the new voters split between the parties in almost exactly the same way as before 1982. The same was true of Delaware and Kentucky, both of which saw a surge of new voters but no change in the partisan balance. A number of other states experienced huge increases in registration over the past two years, but, because registration is nonpartisan, it is impossible to determine which party came out ahead.

In Texas, where both parties and numerous other groups actively signed up new voters under liberalized registration rules, the number of voters went from 6.4 million to 7.9 million in just two years, a 23 percent increase.

That rate was nearly matched in Virginia, where registration went from 2.23 million to 2.67 million, a 19 percent increase.

In Washington state, 336,039 new voters were added to the rolls, bringing the total to 2,441,602, an increase of 16 percent.