"Serbia has not nor it will export weapons to Ukraine," Vucic told reporters, according to the Beta news agency.
He added that the Balkan nation, a traditional Russian ally, "has not nor will it" send ammunition to either Ukraine or Russia.
"There is no paper that would show something like that," he added.
On Wednesday, Reuters was the first to report on the classified Pentagon document, which alleged that Serbia "has agreed to supply arms to Kyiv or has sent them already".
Reuters said it could not independently verify the document's authenticity.
Serbian Defence Minister Milos Vucevic quickly rejected the allegations and said his country "has not and will not sell weapons to either Ukraine or Russia".
"Someone obviously aims to drag Serbia into that conflict, but we adhere to our policy consistently," he said in a statement.
The leaked Pentagon report is a summary of European governments' responses to Ukraine's requests for military training and "lethal aid", according to media reports.
Apart from Belarus, Serbia is the only European nation that has not joined Western sanctions against Moscow.
But the country, which aspires to join the European Union, has backed several United Nations resolutions against Russia over its invasion of Ukraine.
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