Austrian conservative leader Sebastian Kurz has said he will try to form a coalition government with the right-wing Freedom Party after winning this month's election.

Mr Kurz's People's Party and the Freedom Party campaigned for tougher immigration controls, quick deportations of asylum-seekers whose requests are denied and a crackdown on radical Islam.

Austria's president tasked Mr Kurz on Friday with forming a government.

Mr Kurz said that after meetings with all the other parties in parliament he decided to invite the Freedom Party to enter talks on a coalition - a decision that was widely expected.

He told reporters that his prospective partner, Freedom Party leader Heinz-Christian Strache, had shown "a will to bring about change in Austria together".

Mr Kurz, 31, is foreign minister in the outgoing government under Chancellor Christian Kern, a centre-left Social Democrat, and is on track to become Europe's youngest leader.

He said he will try to form a government by Christmas. His party finished first in the October 15 election, but no party was close to a parliamentary majority on its own.

He said a "basic condition" for the new administration is "a clear pro-European direction".

"Austria can only be strong if we are not just members of the European Union, but also actively help to strengthen the European Union," he said.

Austria will hold the EU's rotating presidency in the second half of next year.