Peter Magyar, head of the opposition Tisza party, said no foreign country had the right to interfere in Hungary's vote.
"This is our country. Hungary's history is not written in Washington, Moscow or Brussels, but it is written on Hungarian streets and squares," he wrote on Facebook, adding: "Five days left."
Vance, who described Hungarian Prime Minister Viktor Orbán as his "good friend" before departing the US, joined a rally in central Budapest on Tuesday afternoon.
Hungary's Foreign Minister Peter Szijjártó called the visit proof of a "golden age" in US-Hungarian relations, while a government spokesman described it as "historic."
The trip follows a pattern of public support from the Trump administration for Orbán ahead of Sunday's vote.
In February, US Secretary of State Marco Rubio told Orbán in Budapest: "President Trump is deeply committed to your success because your success is our success."
Most independent polls show Magyar's Tisza party with a substantial lead over Orbán's Fidesz in the run-up to election day, while government-aligned surveys put Fidesz ahead.
Orbán has long been at odds with European Union institutions over his government’s energy ties with Russia and his resistance to EU sanctions on Moscow, among other points of contention.
(ał/gs)
Source: PAP