BUDAPEST (Reuters) - Hungarian political newcomer Peter Magyar's Tisza party is welcome to join the centre-right European People's Party in the European Parliament, the EPP's leader said on Friday.

Magyar has emerged as a new threat to Prime Minister Viktor Orban's iron grip on Hungarian politics with his promises to tackle state corruption and restore democratic checks and balances he says have been eroded during Orban's 14-year rule.

His centre-right Tisza party won seven of Hungary's 21 seats in the European Parliament in Sunday's pan-EU election, more than the rest of Orban's other challengers combined. Orban's Fidesz and its small Christian Democrat allies won 11 seats, down from 13 before the election.

"I can assure you that the EPP family's door is wide open for the Tisza party to join the EPP group," its leader Manfred Weber told a news conference in Budapest.

"The final decision is not in my hands but the group decides about this next Tuesday, I will tell them back home what I saw here," he added.

The EPP remains the largest grouping in the new European Parliament. Fidesz had also been in the EPP but they parted ways in 2021 over Orban's democratic track record and it has not joined any other larger grouping.

Magyar indicated before Sunday's election that if his party won seats, it would aim to sit in the EPP grouping as it would give them the best chance to work for Hungary's interests.

"We will be there with you, and we will build a constructive relationship... Sometimes we will be critical, we have sensitive topics regarding Hungary, but we will be ready... for discussion and dialogue," Magyar told the same news conference on Friday.

Magyar himself will not take up his seat in the EP because he wants to remain in Hungary and lay the groundwork to defeat Orban in the next national election due in 2026.

He has said Tisza MEPs will focus on "bringing home" European funds for Hungary that have been frozen over EU concerns about the rule of law and democracy under Orban's rule.

On Friday Orban told public radio that Fidesz would happily join a new right-wing grouping in the European Parliament if political leaders such as Italian Prime Minister Giorgia Meloni and France's Marine Le Pen could bury their differences.

(Reporting by Boldizsar Gyori, additional reporting by Alan Charlish; Editing by Gareth Jones)