Jansa said Sunday that his support for any of the two candidates in the second round will depend on their endorsement of the reform package.
Both Turk and Pahor have criticized Jansa's government. But they also have called for unity in the face of the crisis.
"Slovenia is a country for all ... our mutual obligation and our mutual responsibility," the 60-year-old Turk said upon casting ballot on Sunday.
Pahor, 49, has said his aim is to restore confidence among politicians and people in Slovenia. Pahor served as the prime minster from 2008 until last year when his government fell over deepening economic troubles paving the way for a snap parliamentary vote last December.
Slovenia has been hit hard by the global economic downturn and the debt crisis in the eurozone. Once a prosperous EU newcomer, the former Yugoslav republic has been tipped as the next country that could seek outsiders' financial help, joining a list that includes Greece, Ireland, Spain, Portugal and Cyprus.
But many voters hope things can improve.
"I think it will be better," said Miro Pogavc, a 75-year-old retiree, as he cast ballot in the capital, Ljubljana. "Less fighting among us, and a better life. That's my opinion."
Turnout at Sunday's balloting was expected to be around 47 percent.
Jovana Gec contributed from Belgrade, Serbia, and Amer Cohadzic in Ljubljana.