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International monitors said Monday's vote was an improvement on recent elections in Armenia but there was little competition as some of Sarksyan's most prominent rivals did not run, saying the result was likely to be skewed to deliver him victory.
The rally in Yerevan's Freedom Square was peaceful and there were no protests in other cities in the ex-Soviet republic. But analysts are concerned about instability in a region that is a key transit route for Caspian gas and oil deliveries to Europe.
Backers of Sarksyan's second-placed rival Raffi Hovannisian chanted "Raffi! Raffi!" and "Armenia! Armenia" at the rally, alleging that the vote was rigged in favour of the Sarksyan.
"We should carry on our fight calmly and according to the constitution. Our democratic movement will not stop and we will achieve victory," Hovannisian told the crowd, raising a clenched fist over his head.
"Welcome Armenia! You are the people, you have chosen your servant," U.S.-born Hovannisian, accompanied by his wife and son, said to the protesters, who were waving Armenian flags.
Hovannisian told protesters that the president, at a meeting on Thursday, rejected his demand for a rerun of the vote.
Official results showed Sarksyan winning 58.6 percent of the votes, compared to nearly 37 percent for Hovannisian.
Hovannisian said he would start touring cities and villages where he polled ahead of Sarksyan in the election, before staging another protest rally in the same square on Sunday.
"There is a 'tradition' in post-Soviet countries that those who scored second or third positions always question results of elections, no matter what," said analyst Sergei Minasyan.
"I think Raffi Hovannisian is aiming for a long march that would somehow unite the opposition to keep up the pressure and maybe benefit from it in the approaching elections for local governments, including for the Yerevan mayor."
The disputed result of the 2008 presidential election triggered violent unrest in which 10 people were killed.
Armenia, a South Caucasus country of 3.2 million that has a collective security deal with Russia, is also locked in dispute with neighbour Azerbaijan over the enclave of Nagorno-Karabakh.
About 30,000 people were killed in a 1990s war between the neighbours over Nagorno-Karabakh, an ethnic Armenian-majority enclave inside Azerbaijan, which Armenian-backed rebels wrested from Azeri troops.