Kenneth Roth, executive director of the New York-based group, took aim in particular at remarks May made to supporters yesterday questioning limits imposed by human rights laws on tackling violent extremism.
"As if George W Bush never happened, UK promotes the canard of rights abuse protecting from terrorism," Roth wrote on Twitter.
He was referring to tough measures passed in the aftermath of the September 11 attacks of 2001, including controversial data collection powers given to the US National Security Agency and the opening of the Guantanamo Bay prison in Cuba.
"And if our human rights laws stop us from doing it, we will change the laws so we can do it," she told supporters, in a message she later repeated on Twitter.
Her comments came ahead of tomorrow's general election, with security issues dominating the campaigns.
May has faced criticism for her record in the six years she served as Britain's interior minister before becoming prime minister last year.
Opposition leader Jeremy Corbyn took aim at May's response, saying: "We will always keep the law under review, but don't believe would-be terrorists and suicide bombers will be deterred by longer sentences or restricting our rights at home."
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