Viktor Orban, Hungary's authoritarian leader, election victory hailed by Putin
His right-wing Fidesz party had 67.8% of the votes, with almost 99% counted.
The opposition alliance led by Peter Marki-Zay was far behind with 28.1%.
The Kremlin says Mr Putin expressed confidence that the two countries could develop further ties "despite the difficult international situation".
In his victory speech, Mr Orban criticised Brussels bureaucrats and Ukraine's President Volodymyr Zelensky, calling them "opponents".
Mr Zelensky has repeatedly criticised Mr Orban's ban on the transfer of arms to Ukraine, with which it shares a border.
Based on preliminary results, the National Election Office said Fidesz would have 135 seats, a two-thirds majority, and the opposition alliance would have 56 seats.
The victory will be Fidesz's fourth successive win since 2010.
Mr Orban, 58, has had a fraught relationship with the EU, which considers that Fidesz has undermined Hungary's democratic institutions.
The BBC's Nick Thorpe in Budapest says that while Hungary has welcomed more than half a million refugees from Ukraine and has joined EU sanctions on Russia, Mr Orban has been cautious in his criticism of Moscow and insists that there should be no attempt to block the sale of Russian gas and oil to Europe.
Several other EU countries, including Germany and Austria, are also wary of sanctioning Russian fuel, and Mr Orban can be expected to seek their support for his position, our correspondent adds.
Mr Marki-Zay admitted defeat late on Sunday evening.
He said the opposition had done "everything humanly possible", but the campaign had been "an unequal fight" as anti-Fidesz politicians had got so little showing in state media.
European election observers say the election, though well run, was marred by the lack of a level playing field for candidates.
"The pervasive overlap between the governing party's campaign messages and the government's communications tilted the playing field," said Jillian Stirk, an official from the Organisation for Security and Co-operation in Europe.
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