"Shahram Amiri left US soil ... for Iran following efforts taken by the Islamic Republic of Iran and the effective cooperation of the Pakistani," Mehmanparast said.
Iran and the US have no diplomatic relations, so Tehran's interests in Washington are handled by a separate "interests section" at the Pakistani embassy.
Repeating accusations that Amiri was kidnapped by US agents, Mehmanparast said Iran would continue to pursue his case "legally and diplomatically".
Washington denied kidnapping Amiri and said he had "lived freely" in the US, with Hillary Clinton, the US secretary of state, saying: "He's free to go, he was free to come. Those decisions are his to make."
Iranian authorities have repeatedly said that Amiri was seized by the CIA as he visited Saudi Arabia last year, and Iranian state television broadcast the text of what it said was an interview with Amiri.
He was quoted in the interview as saying that he was abducted at gunpoint by US agents, while attending the Hajj pilgrimage in Saudi Arabia.
"He's free to go, he was free to come. Those decisions are his to make"
US secretary of state
"There were three people in the van - a driver, another person in a formal suit and beard, and a third person in the back.
"When I opened the door to get in and sit down, the person at the back put a gun to my side and said 'please be quite, don't make any noise'," he was quoted as saying.
PJ Crowley, a spokesman for the state department, said on Tuesday that Amiri had been living in the US for "some time".
"I'm not going to specify for how long, but he has chosen to return," Crowley said.
'Defeat for US'
Iran's semi-official Fars news agency said Amiri was handed over to the embassy by US agents, calling it a defeat for US intelligence services.
"Because of Iran's media and intelligence activities, the American government had to back down and hand over Amiri to the embassy on Monday night," Fars said.
"When I opened the door to get in and sit down, the person at the back put a gun to my side"
Iranian nuclear scientist
Amiri was quoted in the interview as saying: "They intended to send me back home without much noise in order to cover up the kidnapping through denying the whole case, but they couldn't do that in the end."
When Clinton was asked about the case, she chose instead to focus on the fate of American citizens detained in Iran.
"Iran holds three young Americans against their will and we reiterate our request that they be released and returned to their families on a humanitarian basis," she said.
Sarah Shourd, 31, her boyfriend Shane Bauer, 27, and Josh Fattal, 27, were arrested last July along the Iran-Iraq border and accused of espionage.
Their families say they were simply hiking in Iraq's largely peaceful mountainous northern Kurdish region and that if they crossed the border, it was accidental.