Szijjártó will travel on to Eisenstadt, where he will meet Hans Niessl, governor of the Austrian province of Burgenland, for talks on the same topic.
The minister will hold talks in Vienna with Deputy Prime Minister Heinz-Christian Strache and Foreign Minister Karin Kneissl, the statement said.
Crossing by car to Austria continues to be unrestricted at 29 out of the 39 border crossing points whereas crossing options at the remaining ten will be discussed by a joint working group next week, Szijjártó told a press conference after the meeting.
Hungary has enacted measures to prevent illegal entry, he said, and insisted that Austria would not need to put any further restrictions in place at its borders.
The foreign minister said that the two countries have won EU funds to develop five additional border crossing points at one of which preparations for a rail link were under way.
Niessl noted that the implementation of 27 border crossing projects worth 57 million euros was currently under way.