Austria's conservatives and Greens said Sunday they aimed to conclude talks next week to form a government, which would mark the first time the ecologist party will rule at the national level.

Sebastian Kurz of the People's Party (OeVP) has wooed the Greens since his coalition with the far-right fell apart in a graft scandal in May and snap elections allowed both his centre-right party and the ecologists to make gains.

Kurz, 33, and Greens chief Werner Kogler said they aimed to conclude negotiations by the middle of next week.

"The finishing line hasn't been passed yet, but the big rocks on the way to forming a government together have been moved out of the way by both sides," Kurz said in a joint statement with Kogler to the Austrian news agency APA.

Kogler said a "few important questions" remained to be solved, though many seemingly "unbridgeable" problems had already been worked out.

The Greens will hold a party congress - necessary to sign off on any coalition agreement - on January 4.

Kogler confirmed the congress would decide on the "Greens' entry into government" provided the successful conclusion of talks before then.

Both men did not give any details which issues had been solved and what remained open between the two parties.

The OeVP - known for its tough stance on migration and pro-business approach - gained 37.5% in the September polls, while the Greens secured their best-ever result with 13.9%. They are expected to press for a stronger line on climate change, including imposing higher eco-taxes.

Kurz's previous administration - a coalition between the OeVP and the far-right Freedom Party (FPOe) - came crashing down in May after just 18 months as a result of a corruption scandal that engulfed the junior partner.

The FPOe suffered heavy losses during the September election, while the Greens made big gains due to the environment becoming the top voter concern. 

A caretaker government has ruled the country of 8.8 million inhabitants since the previous coalition fell apart.