By Patricia Zengerle

WASHINGTON (Reuters) - Amid heated debate over Iran policy in the U.S. Senate, one of the leading congressional critics of the international negotiations with Tehran squared off with the country's foreign minister on Twitter.

U.S. Senator Tom Cotton used the social media service to challenge Iranian Foreign Minister Javad Zarif to come to Washington for a debate on Iran's "record of tyranny, treachery and terror" after Zarif mentioned Cotton in remarks at New York Univesity on Wednesday.

Zarif said sanctions would be lifted if there is an international agreement on Iran's nuclear program "whether Sen. Cotton likes it or not."

Cotton, a Republican from Arkansas, also upped the ante with a jab at the Iranian, saying that Zarif "hid" in the United States during his country's war with Iraq in the 1980s.

"Not badge of courage... to hide in US while your country fought war to survive-but shows cowardly character still on display today," Cotton, a former U.S. Army captain, wrote on Twitter.

A spokeswoman for Cotton said the senator had written the Tweets himself.

Zarif responded on Thursday with this message: "Serious diplomacy, not macho personal smear, is what we need."

However, the Iranian official added congratulations on the birth this week of Cotton's first child. "May U and Ur family enjoy him in peace," Zarif said.

Zarif, 55, was a student in the United States in the 1980s.

Cotton, 37, is the youngest member of the U.S. Senate, where he has been serving since January.

In March, Cotton wrote a letter signed by 47 of the 54 Republican U.S. senators warning Iran that any nuclear deal made with President Barack Obama could last only as long as the Democrat remained in office, a highly unusual intervention in U.S. foreign policy-making that angered the White House and Senate Democrats.

(Additional reporting by Louis Charbonneau in New York; editing by Andrew Hay)