Iowa's Democratic primary for governor heads toward Tuesday's finish with abortion still dominating center stage and Soviet President Mikhail Gorbachev in the role of bit player.

Iowa House Speaker Don Avenson (D), riding the endorsement of the National Abortion Rights Action League (NARAL) has moved ahead of his rivals, according to a new poll published in today's Des Moines Register.

After trailing throughout the contest, Avenson now leads his opponents with 32 percent, according to the Register's Iowa Poll. Iowa Attorney General Tom Miller (D), the early favorite and front-runner who has seen his lead disappear because of his opposition to abortion, is second with 25 percent. Banker and farmer John Chrystal, a party activist who has not held elective office, is third with 19 percent.

The rest of those polled are either undecided or support lesser candidates.

The primary has been closely watched as an indicator of the strength of the abortion issue in statewide races, and the surge of support toward Avenson in recent weeks suggests that the abortion-rights forces have been successful in reaching voters with their endorsement message.

Miller, a popular figure within his party, has sought to play down the abortion issue in the campaign, but in the absence of other issues to arouse voters, abortion has come to dominate the coverage of the contest.

NARAL first targeted Miller for defeat, arguing that if he won, the fall election would leave voters without a choice on the issue because Gov. Terry E. Branstad (R), who is seeking reelection, also opposes abortion. Then on May 25, fearing that abortion-rights supporters might divide their votes between Avenson and Chrystal, the group endorsed Avenson.

NARAL mounted a campaign in Avenson's behalf that included television and radio advertising, direct mail aimed at women ages 25 to 45 and a get-out-the-vote effort.

Miller continues to stress his experience and his ties to the party, rolling out a series of endorsements in the final week to offset NARAL.

But he has not countered the NARAL campaign directly, preferring to keep the issue out of the campaign, and some analysts believe the NARAL effort may be enough to tip the election to Avenson, who also has strong support from organized labor.

The race is suspenseful for several reasons. One is potential support from antiabortion voters in Iowa, who played a key role in defeating former Iowa Democratic senators Dick Clark and John Culver more than a decade ago. There is some talk about possible crossover voting by Republicans opposed to abortion, and Iowans for Life Inc. has sent out 60,000 pieces of mail describing -- without explicitly advocating -- the procedures for doing so.

Chrystal, who has criticized NARAL for getting involved in the race, is counting on a different dynamic to boost him on Tuesday. As the non-politician in the race, he is using an outsider's appeal to attract votes, saying in a big television blitz that Avenson, Miller and Branstad represent the old politics.

And in a sign of how the world is changing, he's also using the Soviets. Through his farming background, he has known Gorbachev -- once the Soviet agriculture minister -- for many years, and because of that connection the Soviet government recently asked Chrystal to help it recruit 2,000 Americans to modernize the Soviet food and agriculture industry.

Chrystal, who was endorsed by the Des Moines Register and the Omaha World-Herald, touts the request in one of his ads as an indication that he can do things for Iowa's future. When Gorbachev lands in Minneapolis today, Chrystal will be among those who meet with him there.

"It's a wild card," said John Cacciatore, Miller's campaign manager, of Chrystal's Gorbachev connection. "I've not heard of governors being elected on foreign policy."