Nicolas Maduro told CNN news channel that he was stripped of his travel documents and airplane ticket before being "handed over" to a delegation headed by Venezuela's United Nations ambassador on Saturday.
"I ask Kofi Annan [the UN secretary general] that he speak about this case, that investigations be opened [and] I demand that the US government respect international rights," he said.
Hugo Chavez, Venezuela's president, later said on Venezuelan television that Maduro was detained for allegedly taking part in a failed coup attempt in Venezuela on February 4 1992, that Chavez had led against Carlos Andres Perez, the then-president.
However, Chavez denounced the US allegations as "absolutely false", saying Maduro was not involved in the coup.
"This is a provocation from Mr Devil," Chavez said, referring to his speech to UN general assembly earlier this week when he had compared George Bush, the US President, to the devil.
Maduro, who was also attending UN meeting in New York this week, said in an interview with Venezuelan television that "the situation got worse" when he identified himself as Venezuela's chief diplomat.
"I told the on-duty officials that I was the foreign minister and the situation got worse because they started insulting, yelling and brought a police officer... and they started threatening us," Maduro said.
Jose Vicente Rangel, the Venezuelan vice president, linked the detention with Chavez's "devil" joke at the UN.
"It is an attack against the foreign minister, unheard of, unspeakable in terms of the treatment that people with positions like Minister Maduro deserve," Rangel said.
"There's no evidence to support any of this," Russ Knocke, the US homeland security spokesman said.
"There's no evidence to support the claim that his travel documents were taken away, there's no evidence to support the claim that he was assaulted, there's no evidence to support the claim that he was somehow arrested or taken into custody."
Relations between the two countries have been strained since Chavez's re-election in 2002. Chavez has accused the US of funding opposition groups attempting to oust him from power.