Minister Szijjártó slammed the European Parliament for "totally ignoring the democratic will of the people" through "making it impossible for the third largest party group to take positions".
László Kövér highlighted "traditionally good relations" between the two countries, which he said had been built not only on a historical but also on an economic foundation.
The pair discussed bilateral matters and the impact that Ukraine’s planned accession to the European Union would have on Austria and Hungary.
Péter Szijjártó had consultations with his new Austrian counterpart about continued violations of the ethnic Hungarian community's rights in Transcarpathia and on Ukraine's EU integration endeavors.
On Monday, 7 police officers joined the 18 already serving in Hungary, and their number is planned to come to 48-50 by the end of the month, to conduct joint patrols with Hungarian colleagues.
The working lunch on Tuesday focused on the priorities of Hungary’s EU presidency, economic and border protection cooperation, as well as stopping illegal migration.
Sebastian Kurz said efforts by PM Orbán and Hungary’s current EU presidency “offer us an opportunity to take a step in the right direction, but it should be up to the warring sides to seek out a solution”.
The president expressed his support for plans to open a Hungarian language secondary school in Vienna.
Austria at the start of the year established a special government unit within the Chancellery to help persecuted Christian minorities.
The foreign minister said the cooperation between Hungary’s government and the Austrian right will “contribute to our ability to preserve our sovereignty and bring to a halt the European Union’s federalisation efforts”.
The foreign minister said that Austria was among EU countries that took action against illegal migration.
Since March 1, the road linking Ágfalva and Schattendorf (Somfalva) has been fully blocked for vehicles.
Minister Szijjártó said he had talked to Alexander Schallenberg, his Austrian counterpart, who had indicated that Hungary’s expelling people smugglers was problematic for his country.