The threat was linked to al-Qaida and focused on the Middle East and Central Asia, said Rep. Ed Royce, R-Calif., chairman of the House Foreign Affairs Committee.
State Department officials said Thursday they were acting out of an "abundance of caution."
Spokeswoman Marie Harf cited information indicating a threat to U.S. facilities overseas and said some diplomatic facilities may stay closed for more than a day.
Sunday is a workday in the Muslim world. American diplomatic missions in Europe, Latin America and many other places are closed on Sunday.
Royce said Friday he supported the State Department decision to "protect our personnel on the ground."
The State Department issued a major warning last year informing American diplomatic facilities across the Muslim world about potential violence connected to the anniversary of the Sept. 11 terrorist attacks.
Dozens of American installations were besieged by protests over an anti-Islam video made by an American resident.
In Benghazi, Libya, the U.S. ambassador and three other Americans were killed when militants assaulted a diplomatic post. The administration no longer says that attack was related to the demonstrations.
Copyright 2013 The Associated Press.