In a TV interview last week, US ambassador Andrew Schapiro questioned the staunchly pro-Russian Zeman's wish to be "probably the only EU head of state" to attend the May 9 showcase parade on Moscow's Red Square.
He added, however, that it was not up to him to tell the Czech president what to do.
Zeman is one of a handful of world leaders set to attend the event ignored by most western leaders amid tensions over Russia's role in Ukraine.
"I can't imagine the Czech ambassador to Washington giving travelling advice to the US president," Zeman told the parlamentnilisty.Cz news site.
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"And I won't let any ambassador meddle in my plans to travel abroad," added the 70-year-old leftwinger, in office since 2013 as the first-ever directly elected Czech head of state.
Most western leaders have given Russian President Vladimir Putin the cold shoulder while German Chancellor Angela Merkel has promised to visit Moscow on May 10.
Besides Zeman, those known to be planning to travel to Moscow include Greek Prime Minister Alexis Tsipras and North Korea's Kim Jong-Un as well as the leaders of India, South Africa, Mongolia, Cuba and Vietnam.