Rafet Rama, a lawmaker from Thaci`s Democratic Party of Kosovo, is also running for the post.
Hundreds of opposition supporters are camping out in tents on the main square demanding the government`s resignation and fresh elections.
Thousands of people gathered at Skanderbeg Square in front of the building sheltering Parliament, the government and the president`s office.
Police have been trying to keep a small group of Thaci`s supporters away from the main square. They came out despite Thaci`s call to celebrate at home.
The opposition has disrupted Parliament since September with tear gas, pepper spray, whistles and water bottles to reject a deal between Kosovo and Serbia, reached last year, which gives more powers to ethnic Serbs in Kosovo. The opposition also rejects a border demarcation pact with Montenegro.
As president, Thaci would also deal with a special war crimes court created last year, which will have international judges and prosecutors to try ethnic Albanian guerrillas for the alleged killing of civilian detainees, most of them Serbs, immediately after the war ended in 1999.
Thaci was mentioned in a 2010 Council of Europe report which claimed that leaders of the now disbanded Kosovo Liberation Army were responsible for the deaths of hundreds of Serbs, Roma and ethnic Albanians suspected of collaborating with Serbs. Thaci denies the claims.
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