BUDAPEST (Reuters) - Hungarian Prime Minister Viktor Orban's political director congratulated J.D. Vance on being nominated as the running mate of Republican presidential candidate Donald Trump, saying a "Trump-Vance administration sounds just right".

Trump selected J.D. Vance, a U.S. senator from Ohio and a staunch conservative as his running mate on Monday, which could help boost turnout for Trump in the Nov. 5 election, particularly in some of the "Rust Belt" states.

"Congratulations to @JDVance1 on being appointed by @realDonaldTrump as his running mate!" Balazs Orban, who is not related to Viktor Orban, wrote on social media site X on Monday.

Vance had previously voiced support for some of the policies of the nationalist government of Viktor Orban, including legislation that set up foundations to take over the running of universities which some critics said could jeopardise academic freedoms.

In an interview with the European Conservative in February, Vance said that "the closest that conservatives have ever gotten to successfully dealing with left-wing domination of universities is Viktor Orbán's approach in Hungary".

Prime Minister Orban met his long-time ally Trump in Florida last week after the NATO summit and discussed the "possibilities of peace" as Orban pushes for a ceasefire in Ukraine.

Hungary's President Tamas Sulyok met former U.S. ambassador to Hungary David Cornstein in Budapest on Monday where they concluded that they were "ready to act" in order to develop bilateral relations, Sulyok's office said in a statement.

Cornstein served as Trump's ambassador in Budapest between 2018 and 2020.

(Reporting by Anita Komuves; editing by Miral Fahmy)