"I suggested to them earlier that they shouldn't go to Ikea and buy furniture because they won't be staying long," Magyar told a press conference in Budapest on Monday as he set out his government's priorities.
Both Polish politicians were granted international protection in Hungary under Viktor Orbán's government, according to media reports.
Polish prosecutors have charged them in connection with irregularities involving the Justice Fund, a state fund overseen by the justice ministry in Warsaw.
A European arrest warrant has been issued for Romanowski, while a separate warrant request for Ziobro is currently before a Polish court.
Magyar said Hungary "will not be a dumping ground for criminals wanted by the international community" and reiterated his pledge to extradite them in line with international law and European cooperation principles.
With nearly 99 percent of votes counted, Tisza secured 138 seats in Hungary's 199-seat parliament – a two-thirds constitutional majority.
Orbán's Fidesz-KDNP coalition won just 55 seats.
Voter turnout reached nearly 80 percent.
Magyar said he received a phone call from Polish Prime Minister Donald Tusk, who expressed satisfaction that Hungary would "return to Europe."
He pledged to visit Warsaw in early May as his first foreign trip as prime minister, calling it a step toward rebuilding the "thousand-year Polish-Hungarian friendship."
He also announced Hungary would rejoin the European Public Prosecutor's Office and the International Criminal Court – both moves reversing Orbán-era policies – and said joining the eurozone was in Hungary's interest.
Magyar additionally accused outgoing Foreign Minister Péter Szijjártó of destroying documents related to Russia sanctions at the foreign ministry on Monday morning, saying: "We know that the destruction of documents began a few days ago – like in the old days."
(ał/gs)
Source: PAP