Polish government leaders condemned two self-described radical nationalist groups seeking an ethnically and religiously pure country that organized an Independence Day event attracting tens of thousands of people.

“We do not approve of support in the public sphere for an ethnic national community, we support the idea of a nation rooted in culture,” Piotr Glinski, the country’s deputy prime minister said on Sunday, a day after the country’s largest national independence celebration attracted far-right movements from at least...