Turkish President Recep Tayyip Erdogan travelled to Hungary to meet Prime Minister Viktor Orban on Sunday, with talks on energy security and Sweden's membership of Nato on the agenda for both countries.
Turkey had had long blocked Sweden's membership before lifting its veto last month but Hungary is yet to approve its entry into Nato.
"We can come back to the issue at the autumn session," Hungary's Foreign Minister Peter Szijjarto said on Facebook as both countries' parliaments are on holiday.
"We have agreed to stay in touch."
The two countries have also discussed strengthening their energy co-operation. Hungary already receives a large proportion of its gas through the TurkStream pipeline, which carries Russian gas across the Black Sea.
Budapest and Ankara will also be deepening their "strategic partnership", an announcement due to be made official during a visit by Mr Erdogan scheduled for December.
The Turkish leader's visit is part of a series of diplomatic meetings organised by Mr Orban to mark the World Athletics Championships, which opened on Saturday.
Among other dignitaries welcomed on Sunday were the presidents of Serbia, Azerbaijan, Kyrgyzstan as well as President Serdar Berdymukhamedov of Turkmenistan.
Mr Szijjarto welcomed "the close co-operation between Central Asia and the Western Balkans", which he said was especially important given the energy crisis.
Serbia has promised to "provide the necessary transit capacity" if Ukraine decides to stop allowing Russian gas to pass through its territory on its way to European countries, he added.
An agreement was also signed with Azerbaijan on storing 50 million cubic metres of gas on Hungarian soil.
Hungary, the only country EU member state to have maintained links with the Kremlin since the beginning of the Ukraine war, has in recent years pursued a policy of opening up to the East, not only towards Russia, but also towards Central Asia and China.
Mr Orban was delighted to welcome his "political friends" at the weekend. Hungary's western partners, who regularly accuse him of authoritarian excess, were not present.