Relations between Russia and the West soured after Moscow annexed Crimea from Ukraine in March 2014 and backed pro-Russian separatists in the east.
NATO members including Poland and the Baltic states have voiced concern that they could be targets of hostile acts from Russia, and last month NATO leaders agreed to deploy military forces and to increase air and sea patrols there.
"I don't think it is a realistic assumption today that Russia would attack any NATO member state," Hungarian Foreign Minister Peter Szijjarto said in an interview with news portal Index.hu.
Szijjarto said each NATO member state had feelings of "different intensity" about a perceived threat from Russia, and that he respected other views.
"This is not how we feel about Russia. I don't think Russia would pose an existential threat to us," he said.
Prime Minister Viktor Orban's conservative government has granted a deal to Russia's Rosatom to build new reactors at Hungary's nuclear power plant, and has promoted what it calls a "pragmatic" relationship with Russia.
The Czech Republic and Slovakia also have less fraught relations with Russia. Slovak Prime Minister Robert Fico has called for a removal of the sanctions imposed by the West over Russia's role in Ukraine.
But tensions flare up intermittently. Bulgaria's defense minister last month accused Russia of growing airspace violations, describing them as "provocations toward Bulgaria and its air forces".
When asked about Turkey, Szijjarto -- who had earlier described the failed coup in Turkey as a "terrorist act" -- said he did not see any anti-democratic developments in Turkey.
The scale of President Tayyip Erdogan's crackdown on the military, judiciary, civil service and schools since the July 15-16 coup - has unnerved Turkey's NATO allies.