Zakkharova mocked Vucic in a comment on the Facebook post, saying he was invited to the White House to be interrogated.
Vucic and other Serbian officials reacted furiously.
“The primitivism and vulgarity she showed speaks about herself, but also about those who have given her the job,” Vucic told the pro-government Pink TV.
Vucic said while he was in Washington he defended Serbia’s close ties with Russia, including an arms purchase, and his refusal to impose Western sanctions against Moscow over its policies in Ukraine.
Marko Djuric, an official with Vucic’s ruling party, defended him on Twitter.
“This president did not say a single bad word against Russia, not even in that place (the White House.) ... I will not allow you to attack proud Serbia. Shame on you!” Djuric wrote.
Although formally seeking membership in the European Union, Serbia under Vucic has been forging close political, economic and military ties with Russia and China.
Trump announced Friday that former wartime foes Serbia and Kosovo have agreed to normalize economic ties as part of U.S.-brokered talks that include Belgrade moving its Israeli embassy to Jerusalem, and mutual recognition between Israel and Kosovo.
The announcement provided Trump with a diplomatic win ahead of the November presidential election and furthers his administration’s push to improve Israel’s international standing.
The agreement also calls on Serbia to diversify its energy supplies, which are now fully in Russia’s hands — something unlikely to be approved by Moscow.