Appearing alongside British foreign secretary Boris Johnson in London, Mr Tillerson said that "all across America, hearts are broken" at news of the attack on people attending a concert by US pop singer Ariana Grande.
British police briefly suspended intelligence sharing with the United States on Thursday after private details of their investigation repeatedly appeared in American media.
"We take full responsibility for that and we obviously regret that that happened," Mr Tillerson said. "With respect to the release of information inappropriately ... certainly we condemn that."
Mr Tillerson said he expected the close security relationship between the United States and Britain to withstand the leaks.
(Reporting by William James, writing by David Milliken, editing by Paul Sandle)
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