His erstwhile coalition partners, the scandal-hit far-right Freedom Party (FPOe), meanwhile, dropped from nearly 26 percent at the last election to around 16 percent.
A three-way pact with the Greens (which received 12.4 per cent of the vote) and the liberal pro-business Neos party (7.4 per cent) is considered far more likely than a grand coalition with the Social Democrats (21.5 per cent).
"We want to improve our result", Mr Kurz told reporters before casting his vote in Vienna, referring to the 31.5% his People's Party (OVP) achieved in 2017.
With almost all the votes counted, Mr Kurz's party has more than 38% of the vote, up from 31% last time round.
"We vote to decide in which direction we will go - that of Orban and the populists, or if we stay oriented towards Europe. we decide if the corruption will go on", said Vienna voter Gabriel Steiner, 29. The Greens were big winners amid voters saying the climate was their top concern, securing at least 13 per cent of the vote.
But the Freedom Party has seen a drop in support.
The People's Party triumphed in eight of Austria's nine federal states, losing only Vienna to the Social Democrats.
About 6.4 million Austrians aged 16 and older were eligible to vote.
Polling stations across Austria will open at 07:00 local time (05:00 GMT) and close at 17:00 (03:00 GMT).
SPO boss Pamela Rendi-Wagner said that this was only a preliminary result, but admitted "that's not what we wanted".
Kurz, 33, has not ruled out any coalition partners and has said he will speak to all parties in parliament.
While some commentators think it would make sense for him to join forces with the Greens and perhaps the liberal Neos, the Greens fear Kurz will use them as a stalking horse to then land up back in bed with the FPO. Impacted by "Ibiza scandal" and another affair surrounding former party leader and ex-vice chancellor Heinz-Christian Strache, the party got only 16 percent of the votes.
"We did not receive a clear mandate to continue the coalition", the European Union parliamentarian said.
"We can not undo everything that has been done", the Greens leader Kogler said before the elections.
For example, a partnership with either the SPOe or the Greens would be hard to explain to the some 258,000 voters who are estimated to have switched to Kurz from the far-right.
For nearly four months, the country has been ruled by former Constitutional Court head Brigitte Bierlein - appointed chancellor by President Alexander Van der Bellen - and the interim government she formed with high-level bureaucrats.
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