The exploitation of Mongolia's vast coal, copper and gold reserves has helped transform an economy once characterised by nomadic lifestyles not far removed from its famous empire-building hero, Genghis Khan, 800 years ago.
But rising inequality in the cities and environmental damage in rural areas are dominating the political debate, while recent falls in commodity prices and slowing demand in the key market of China have sparked uncertainty ahead of the election.
"Let the blessings be upon the people," added the incumbent, a former journalist who played a leading role when Mongolia peacefully threw off 70 years of communist rule in 1990.
Voters appeared to be out in force in the hours after polls opened at 7:00 am, with national television showing huge queues in some polling stations.
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Voter turnout by around mid-afternoon was 43 percent amid heavy rains in some regions that hindered road travel, according to the General Election Commission (GEC), though the figure was about the same as the last presidential election in 2009. Final turnout for that vote came to about 73 percent.
Accusations of vote-rigging in 2008 parliamentary elections resulted in deadly riots, and led to Mongolia adopting an electronic voting system.
But GEC chief Sodnomtseren Choinzon said the computer problems were confined to two voting stations and were "not widespread".
Results of parliamentary polls last year were delayed by complaints about the electronic system. However, the election was largely considered a success.
Recent polls suggest that Elbegdorj, who became president in 2009 after twice serving as premier, will secure a second term to continue his policy of using foreign cash to drive the rapid development of Mongolia's economy, which is galloping ahead at double-digit rates.