The outstanding votes are due to be tallied by mid-week. According to some of the polls, FPOe is expected to gain many votes in the election, becoming either the second or third largest party.
The projections showed the center-left Social Democrats receiving 26.6 percent and the vote and the anti-migrant, euroskeptic Freedom Party 26.5 percent.
Despite the predicted win, Kurz will still need to establish a coalition, which would likely include the far right-wing Freedom Party of Austria (FPOe), led by Heinz-Christian Strache.
Although the Social Democrats have come either first or second in elections since World War II, voters are now more receptive to calls for tougher migration rules than the party's focus on social justice. Social Democratic Chancellor Christian Kern acknowledged as much, saying Sunday's results reflected "a push to the right".
The incredibly close result puts foreign minister Sebastian Kurz, 31, on track to become Europe's youngest head of government.
Much of the People's Party's appeal has been credited to Kurz.
An ORF opinion poll said 40 percent of OVP voters favor a coalition government with the FPO, while only 18 percent support a coalition with the Social Democrats.
Strache has modified the tone of his message when speaking to the broader public.
"Right-wing parties in governments. exist in other European states as well", said the 60-year-old.
Others that may clear the 4 percent hurdle needed to get into parliament seats are the Greens, the liberal NEOS, and Liste Pilz, led by former Greens politician Peter Pilz.