"Today I sent an invitation letter to Prime Minister Ulf Kristersson for a visit to Hungary to negotiate on Sweden’s NATO accession," Orbán wrote on X, formerly Twitter, DPA international reported.
Hungary and Turkey are the only members of the 31-nation alliance that have yet to approve Sweden's request to join.
Orbán's message came on the same day that the Turkish parliament is scheduled to vote on Sweden's accession.
In Hungary's parliament, the vote is now only a formality as the relevant committees have already gave the green light.
But the final vote has been repeatedly postponed at Orban's instigation, out of anger at criticism from Stockholm about the state of the rule of law in Hungary.
Orban has said that Hungary and Turkey are not working together to stall Sweden's application, but that each government had its own concerns.