A rare public dispute has broken out between the president of the Czech Republic and the US ambassador to the central European country.

The dispute started after Ambassador Andrew Shapiro faulted President Milos Zeman for attending a Russian military parade at a time Moscow is being criticised by the US for its involvement in the conflict in eastern Ukraine.

But the Czech prime minister together with legislators are siding with the American.

In an interview with online publication Parlamentni Listy on Sunday, Zeman bristled at the envoy's implied criticism of his decision to attend Moscow's traditional May 9 military parade.

Zeman said Shapiro was no longer welcome in the Prague Castle, the seat of presidency.

"I think that the reaction of President Zeman was not adequate," Prime Minister Bohuslav Sobotka said.

"I would naturally welcome it if the attitude of Mr President to foreign policy in general was a bit more professional," Sobotka told the Czech public television on Monday.

"We should be able to communicate with our friends and allies," Sobotka added.

Parliament's lower house speaker, Jan Hamacek, said he thought Zeman was overreacting and the deputy speaker of Parliament's upper house, Premysl Sobotka, said Zeman demonstrated a lack of "diplomatic thinking".

Jan Mlejnek, an analyst, said Zeman's rhetoric was unfortunate and will harm Czech-US relations.

In an emailed statement from the US embassy, Shapiro said "it would be unfortunate for President Zeman to be there as perhaps the only EU head of state."

Zeman, whose is critical of European Union sanctions against Russia, said he wanted to honour Soviet soldiers who sacrificed their lives to liberate his country in World War II.

The Czech presidency is a largely ceremonial post.

Sobotka said he accepted Zeman's explanation for the trip.

Shapiro said he regretted that Zeman felt offended.

"I value a good working relationship with everyone, and I want him to know that my door will be open to him,"? Shapiro said. "I also want the Czech people to know that the United States government, and the people of America, value our relationship as partners and allies more than ever."