The election for the largely ceremonial post is being held as the recession-hit country struggles to stave off a bailout and plug the gap in its public finances, with a budget deficit of 4.2% of gross domestic product expected this year.
"It seems very likely that Pahor will win in the second round. What may have convinced the voters was his bridge building between the government and the opposition," Borut Hocevar, a political analyst from daily newspaper Finance said.
Pahor, from the center-left opposition Social Democrats, won 40% of the votes. Türk, an independent backed by the larger center-left Positive Slovenia opposition party, won 36%.
The presidential candidate from Prime Minister Janez Janša's ruling conservative coalition came a distant third.
Pahor served as prime minister from 2008 till 2011 when his government was ousted by parliament after a series of its reform laws were rejected at referendums demanded by trade unions, students' unions and the opposition.
This led to early election which brought Janša to power.
Export-oriented Slovenia, which adopted the euro in 2007, is now suffering from lower export demand and a fall in domestic spending amid budget cuts, a rise in non-performing loans held by state-owned banks and unemployment of almost 12%.
Last month, it issued its first sovereign bond this year, averting a bailout for at least six months.
The government plans to reform the banking sector, speed up privatization, raise the retirement age and cut public sector wages and unemployment benefits.
But the opposition and trade unions last month demanded referendums on some reforms, which could stall or reject them.
One of the incoming president's duties will be to nominate a new central bank governor, who will sit on the European Central Bank's governing council after governor Marko Kranjec's mandate expires in June 2013.