Russian Federation launched a failed bid past year to derail Montenegro's negotiations with the bloc.
Montenegro's presidency is a ceremonial post, but is expected to become the real seat of power in the country if 56-year-old Djukanovic wins the vote. Current President Filip Vujanovic is not running due to term limits.
Veteran politician Milo Djukanovic steered to victory with 53.8 percent of the votes in according to a projection by the Centre for Monitoring and Research (CeMI).).
"I also want to congratulate the victory to the newly elected president, Milo Djukanovic", Haradinaj wrote.
Opinion polls indicate he is such a strong favourite that he may be able to win more than half of the votes, which would rule out a run-off planned for April 29.
"I will continue to fight to free Montenegro of Djukanovic and his dictatorship", Bojanic said.
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Sunday's vote passed off peacefully amid fears of disorder after 20 people were arrested and accused of trying to stage a coup during legislative elections in 2016.
The vote is the first since Montenegro joined the western military alliance in December.
Challenger Bojanic, who was backed by several opposition groups, including pro-Russian ones, vowed to continue his struggle against Djukanovic, describing him as "the man holding Montenegro and its institutions hostage".
"I agree with Djukanovic that the state is stronger than mafia".
Djukanovic had claimed the opposition wanted to turn the country into a "Russian province" and threaten Montenegro's multicultural way of life. The results showed that Djukanovic won a large enough percentage to avoid a runoff election.
For Djukanovic, however, the choice between Brussels and Moscow is crucial to Montenegro's development. "Our President will soon appeal to the citizens", - said the head of staff Milos Nikolic.