GUATEMALA CITY (Reuters) - A conservative businessman claimed victory late on Sunday in Guatemala's tense race for president, saying he defeated former military dictator Efrain Rios Montt's bid to regain power.

As official results trickled in, Oscar Berger, the former Guatemala City mayor, told supporters the party's numbers showed he might have won the outright majority needed for an unprecedented first-round victory, amid a record turnout of voters.

If not, he will face the runner-up, left-leaning career politician Alvaro Colom, in a second round in December to decide the Central American nation's second presidential election since 1996 peace accords ended a 36-year civil war.

If Rios Montt, who is blamed for civil war atrocities during his 1982-83 rule, comes in third as Berger claimed and early results indicated, he will be out of the race.

"We have begun to defeat corruption, dishonesty and shamelessness," Berger told cheering supporters. "Today we started to change our Guatemala."

The heavy turnout -- estimated as high as 80 percent -- sparked some violence and delayed the vote count as polling stations stayed open late.

Two indigenous women were crushed to death by crowds in Quiche province while an opposition party campaign director was shot in the leg in the capital. It was unclear if the attack was politically motivated.

Voters flocked to the polls, apparently to oust Rios Montt's ruling Guatemalan Republican Front, or FRG, which is widely seen as corrupt. Early results had him in third place.

While Rios Montt made no public statement, his campaign said he was awaiting results from the countryside, where the party has strong support.

Colom told a press conference he believed he was in a dead heat with Berger, as pre-election opinion polls had predicted.

The race opened war-time wounds and touched sensitive issues of class and corruption in the Central American nation of 11 million people, more than half of them Maya Indians often living in deep poverty.

"GUATEMALA HAS A MEMORY"

Survivors and rights groups blame Rios Montt for massacres in hundreds of Indian villages as part of a "scorched earth" counterinsurgency campaign at the height of the war.

His defeat was a sign that Guatemala "has a memory and has the desire to change," said sociologist Miguel Angel Sandoval, who is helping survivors mount a genocide case against Rios Montt and others.

Though his candidacy fueled tension and violence in the days ahead of the polling, authorities and observers said the balloting for presidential, legislative and municipal posts was largely peaceful, aside from isolated disturbances.

"We didn't see any nails in the road to prevent people from going to the polls and we saw a massive turnout," said U.S. Ambassador John Hamilton.

The United States had expressed strong reservations about Rios Montt, saying he would be difficult to work with, though he had U.S. backing during his 1980s regime.

Observers applauded the turnout as evidence of Guatemalans' growing faith in democracy despite rising political violence, a boom in organized crime and drug trafficking and attacks on journalists, judges and activists.

"The success is that people went out to vote," said Maya Indian leader Rigoberta Menchu, who won the Nobel Peace Prize in 1992. "This first round was to say 'no' to violence."

(Additional reporting by Frank Jack Daniel and Tim Gaynor)