The People's Party (ÖVP) won 31.6 percent of the vote in Sunday's parliamentary elections, marking a major victory for the 31-year-old Kurz, according to the latest vote count by state broadcaster ORF.
If the ÖVP keeps that vote count, they're set to lead parliament with at least 62 seats.
"I can promise you today that I will fight for change in this country with all my power," Kurz told supporters at a rally. "I accept this responsibility with great humility."
The right coalition
The far-right, anti-immigration Austrian Freedom Party (FPÖ) came in third place with 26 percent, amounting to 51 seats, while the center-left Social Democratic Party (SPÖ) managed to garner 26.9 percent, placing them in second with 53 seats.
"It shows that we have arrived at the center of society. We are the ones that dominate the political debate," said FPÖ chief Heinz-Christian Strache.
Kurz's ÖVP is expected to form a government with the far-right FPÖ, after he ended a grand coalition government with the center-left SPÖ earlier this year. It would mark the first time the far-right party enters government since 2000. A final vote count is expected Thursday.
Kurz suggested he is open to talks with other parties. "I would of course like to form a stable government. If that cannot be done then there are other options," Kurz told ORD.
Finance Minister Hans Jörg Schelling, a member of the ÖVP, told DW that the center-right party - as a whole - is open to talks with both the FPÖ and the Social Democrats. Meanwhile, SPÖ chief Christian Kern said he will stay on as his party's leader despite losing to his government's junior coalition partner.
The New Austrian and Liberal Forum (NEOS) picked up 5.1 percent of the vote, amounting to 10 seats, which remains roughly unchanged from the 2013 election.
The Green Party took a beating, losing 8.5 percent compared to the 2013 election. The Greens managed to garner 3.9 percent of the vote, which isn't enough to make it into parliament.
Read more: Germany's Green party: How it evolved
The Greens' lead candidate Ulrike Lunacek said the election result has been difficult to stomach, describing it as a "heavy defeat and a great disappointment." However, an offshoot party led by former Greens member Peter Pilz managed to gain 4.4 percent of the vote, amounting to 8 seats.
Migration: Austria's main concern
Before the elections, campaigning focused on migration, notably the 2015 migration crisis that polarized European politics.
That year, Austria was used as a gateway for nearly 900,000 migrants making their way to Germany. It also received more than 68,000 applications for asylum in 2015, one of the highest proportions on the continent compared to the population.
While the center-left SPÖ campaigned on a track record of lowering unemployment and of economic growth, Kurz's ÖVP promised to prevent a repeat of 2015's wave of migration and cut access to social welfare benefits for newcomers for at least five years.
In a poll by state broadcaster ORF, 55 percent of respondents that voted for the ÖVP said they did so because of their stance on asylum and integration.
ls/sms (dpa, AFP, Reuters, AP)