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Marc Frons, the chief information officer of The New York Times Company, said the internal systems of The Times did not use the flawed version of OpenSSL, and no digital subscribers’ information was at risk.

Mr. Frons said the attacks on Twitter and The New York Times required significantly more skill than the string of S.E.A. attacks on media outlets earlier this year, when the group attacked Twitter accounts for dozens of outlets including The Associated Press.

Mr. Frons said that “we believe that we are on the road to fixing the problem.”

Marc Frons, chief information officer for The New York Times Company, issued a statement at 4:20 p.m. on Tuesday warning employees that the disruption — which appeared to be affecting the Web site well into the evening — was “the result of a malicious external attack.”

“In terms of the sophistication of the attack, this is a big deal,” Mr. Frons said.