"We are extremely pleased with such a convincing win," Enkhbayar's campaign adviser Tjalling Halbertsma said.
"We are relieved also that nobody cried foul. It is a big result for us. It has been an extremely successful campaign."
The president of what was once one of the world's greatest empires, does not have as much direct power as its prime minister, currently Tsakhiagiin Elbegdorj of the Democrats, but does command the armed forces and have influence in the divided parliament.
Enkhbayar, who would replace Natsagiin Bagabandi also of the MPRP, campaigned against Mendsaikhanii Enkhsaikhan of the Democratic Party, Bazarsadiin Jargalsaikhan of the Republican Party and Badarchiin Erdenebat from the Motherland New Socialist Democratic Party.
Final result expected
"From the preliminary information we have, Enkhbayar has won"
An official election result is expected at about 0700 local time. If none of the four candidates wins by more than 50% of the vote, the two highest-placed contenders will compete in a run-off.
After a campaign dominated by promises to end widespread poverty, Mongolians have been voting for a new president among four major rivals.
Voters began lining up even before polls opened at 7am on Sunday, many in traditional Mongolian clothing just for the occasion.
Voter turnout has been typically high in Mongolia - in the last presidential vote it was 83% - a legacy of communist rule before 1990, when voting was compulsory.
Mobile ballot boxes
But unlike under communism, now we can choose, said Janchiv Tserev, 82, who wore his second world war medals pinned to his knee-length maroon tunic.
"Before, we could vote for only one person. Now, there are four candidates," he said.
For elderly nomads too frail to make it to their voting site, poll workers took ballot boxes to them - driving out in 4WD vehicles to the round white tents that dot Mongolia's grasslands.
Election workers took ballot
boxes to elderly nomads
"It's good to be old, because people come out and take our vote," Batsukh Tseveenchimed, 62, said as she offered bread and tea to the six poll workers - including opposition party monitors - who descended on her tent.
"All the candidates sounded the same to me, so I just voted for my old party," she said later of Mongolian People's Revolutionary Party (MPRP), which governed the country under communism.
"We know that party. That's the party that used to rule
Older voters' loyalty to the ex-communist MPRP had helped put its candidate Nambariin Enkhbayar ahead in opinion polls.
The MPRP gave up its monopoly on power in 1990 and has since been voted out and back into power.
Mongolia's economy collapsed after Soviet subsidies ended, and MPRP supporters say they hope the party's experience in government will bring greater stability.
Opposition parties say the
election process is unfair
Opposition parties complain that MPRP members still dominate the local election commissions that register voters and staff the polls.
Activists demonstrated in the capital earlier this month against the election bodies, and said they would be on guard against voter intimidation.
International observers were visiting polling sites on Sunday to investigate any complaints.
The Democratic Party's Mendsaikhanin Enkhsaikhan draws his support from anti-communists, who defied police to take the streets in 1990 and bring down one-party rule.
He advocates direct subsidies to poor families, lower taxes for private businesses, and keeping a larger share of profits from foreign mining operations.
The Democrats are hurt by division within their ranks and the memory of their term in power in, 1996-2000, when a coalition of anti-communist parties splintered and collapsed.
The other two candidates say Mongolia needs an alternative to the larger parties.
The Republican Party's Bazarsadyn Jargalsaikhan is one of the country's richest men. His Buyan Co processes cashmere, and he says his success as a businessman shows he can bring prosperity.
The Motherland Party's Badarchyn Erdenebat supports a national referendum to give more power to the presidency, in a country where parliament is splintered among many parties and the prime minister changes frequently.