Chancellor Sebastian Kurz led his conservative party to victory in Austria's October parliamentary election, then struck a coalition deal with the anti-immigration Freedom Party last month, making Austria the only western European country to have a far-right party in government.
Kurz made a hard line on immigration the core of his campaign after Austria took in one of the biggest contingents of asylum seekers in Europe's migration crisis in 2015, relative to its population. Many of those people came via Hungary until Orban fenced off much of its border with Serbia.
Having taken similarly tough stances on immigration, Kurz and Freedom Party leader Heinz-Christian Strache argued during the campaign over who had better relations with Orban - a nationalist popular at home but frequently criticised by Western leaders and rights groups.
Orban said in a video recorded on the train that took him to Vienna on Monday and posted on Facebook he would meet both men.
"I would like to sign agreements with them ... which should be about migration, about protecting Austria and Hungary and about helping each other. I hope I will succeed." he said.
Strache, who is now vice chancellor, has said Austria should move away from its usual western European allies including Germany by joining the Visegrad group of eastern states, which includes Hungary and Poland. They frequently defy Brussels on issues such as immigration and fundamental rights.
Kurz has sought to reassure allies that his government will be pro-European, even though he and Strache favour a smaller EU that focuses on fewer tasks, especially securing its external borders.
He has sided with Visegrad in saying the EU should stop pushing countries to take quotas of relocated asylum seekers. But he supported the bloc's punitive steps against Poland for threatening the rule of law and democratic principles.
"I think we can be a good bridge-builder within the European Union," Kurz told a joint news conference with German Chancellor Angela Merkel in Berlin this month, referring to the West and Visegrad.
He has, however, taken steps that could complicate a rapprochement with Orban.
Kurz's government is continuing Austria's decades-old policy of opposing nuclear energy, and said this month it would sue the European Commission for allowing Hungary to expand its Paks power plant.
It has also decided to curb child benefits for workers whose children live in poorer countries including Hungary. Visegrad member Slovakia has already objected.
"Austria must not throw in its lot with member states that have left the European path," the opposition Social Democrats' spokesman for Europe, Joerg Leichtfried, said in a statement.
"Viktor Orban and co. are promoting and practicing wage and social dumping," he added, referring to the Hungarians and citizens of other eastern European countries who work in Austria, which the Social Democrats and others say often undercuts local wages and living standards.