The suit was filed by four Zimbabweans whose relatives were allegedly murdered by government supporters in the run-up to parliamentary elections in June.
The plaintiffs are seeking $400m in damages under a 200-year-old American law which gives foreigners the right to file civil suits in US courts for injuries suffered in violation of international law.
The US Government has objected to the suit against President Mugabe, citing concerns that he might be entitled to immunity while on a diplomatic visit. Mr Mugabe's spokesman described the legal action as a "non event."
Election violence
More than 30 people died in the election campaign, nearly all of them supporters of the main opposition Movement for Democratic Change (MDC).
Human rights activist Topper Whitehead said President Mugabe was served with the lawsuit while attending last week's UN millennium summit in New York.
The plaintiffs include an opposition candidate Elliot Pfebve, whose brother was murdered and Maria Stevens whose husband was the first white farmer to be killed during the election campaign.
The suit accuses of Mr Mugabe of resorting to violence so that his party, Zanu-PF could stay in power.
The plaintiffs say they are suing Mr Mugabe in the United States rather than Zimbabwe because of the continuing lawlessness in the country.
But speaking at a Harlem church, President Mugabe insisted that he does not seek revenge against opponents.
He noted that Zimbabwe's last white leader, Ian Smith was left to live.
"If I was a vengeful leader, would he be walking the earth?" Mr Mugabe asked.
Lawlessness
Human rights groups have said President Mugabe's supporters used brutal tactics against the opposition MDC.
As well as seeking damages, the four plaintiffs say they hope to open the eyes of the world to the record of what they call Mr Mugabe's "monstrous regime".
The opposition MDC welcomed the move, saying it provided a reminder to President Mugabe that although the rule of law did not prevail in Zimbabwe, it did in other parts of the world.
Those behind the legal action say they are concerned that it could be met with further violence, but are prepared to live with the consequences in their struggle for justice.