Hofer has also urged his supporters to recognize the victory of his rival, Green Party-backed independent candidate Alexander Van der Bellen.
"I am asking my electorate to recognize that we have a winner. We should stand together supporting our country," Hofer added.
According to the Interior Ministry, Van der Bellen is leading the Austrian presidential election with 60.4 percent of ballots against 39.6 percent received by his rival.
The presidential rerun was called after Austria’s top court overturned the results of May’s election over postal vote irregularities following an appeal from the far-right Freedom Party.
The poll was won by Van der Bellen who defeated Hofer in the runoff by just 31,000 votes. The turnout was estimated at 72 percent, or almost 4.4 million.
