"This is, of course, the choice of the Hungarian people," Nawrocki told reporters on Monday.
"I will cooperate with whoever free nations choose, for the good of Poland."
He added that it was not his role as president to comment on foreign elections, describing the result as Hungary's sovereign decision.
Prime Minister Donald Tusk, speaking from Seoul, also congratulated Magyar, saying the two had spoken briefly about an upcoming visit to Warsaw.
"I think our relations will be absolutely exceptional," Tusk said.
With nearly 99 percent of votes counted, TISZA is on course to win 138 seats in Hungary's 199-seat parliament, the Polish news agency PAP has reported.
The ruling Fidesz-KDNP coalition of outgoing Eurosceptic Prime Minister Viktor Orbán is projected to take 55 seats, with the far-right Mi Hazánk party set to win six.
The result ends 16 years of Fidesz rule in Hungary.
During his time in office, Orbán has shifted markedly from his origins as a centre-right member of the European People's Party, embracing an increasingly nationalist and anti-immigration platform while growing closer to Moscow and more distant from Brussels.
Significant political shift
The election outcome marks a significant shift in the political landscape that Nawrocki had navigated just weeks earlier.
In late March, he met Orbán in Budapest during the two countries' annual Friendship Day, a visit that drew sharp criticism at home.
Critics said the trip could be seen as a show of support for Orbán ahead of the elections, and both Prime Minister Tusk and Foreign Minister Radosław Sikorski condemned the meeting.
Nawrocki said at the time that while Poland and Hungary share common ground on some EU issues, they differ "particularly regarding Russia".
(ał)
Source: PAP