After meeting Czech President Milos Zeman, Hofer said he would like the group — currently comprising the Czech Republic, Hungary, Poland and Slovakia — to also include Austria.
“Norbert Hofer presented his project of 'a Union within the Union',” said
Zeman's spokesman Jiri Ovcacek.
Hofer and veteran left-winger Zeman focussed their discussion on migration into Europe, which they both condemn.
The Visegrad countries have all taken a hard line on the huge influx of
refugees and migrants to Europe since last year.
Ovcacek said the pair did not talk about the post-war Benes decrees
expropriating and expulsing so-called Sudeten Germans from the borderland regions of the former Czechoslovakia, which split into two countries in 1993.
Austria and Germany have called the decrees discriminatory, while the Czech Republic and Slovakia say they were justified retaliation against Germany after World War II.
In a newspaper interview before his visit to Prague, Hofer said the decrees were an “injustice”.
Hofer came in a narrow second in Austria's May presidential election. He challenged the result in court and the vote was annulled.
On Monday, the Austrian government announced the new vote would be postponed from October 2 to late November or early December because of glue failing to stick on postal votes.