The US has issued a worldwide travel alert for its citizens in response to "increased terrorist threats".
The state department said "current information" suggested the Islamic State [IS] group, al-Qaeda, Boko Haram and others continued "to plan terrorist attacks in multiple regions".
The alert, it said, will remain in place until 24 February 2016.
France, Russia, Mali and several other countries have seen deadly attacks in the past month.
A US state department representative told BBC News there was "currently... no reason to believe that US citizens would be specifically targeted".
Meanwhile Belgium announced the capital Brussels would stay at the highest level of alert for another week over fears of militant attacks like those that killed 130 people in Paris on 13 November.
In other developments
-- An apparent explosives belt was found in a bin in the Paris suburb of Montrouge, which a fugitive suspect is believed to have passed through on the night of the Paris attacks
-- France carried out its first air strikes against IS from its Charles de Gaulle aircraft carrier, newly deployed in the eastern Mediterranean, reportedly hitting targets in Iraq and Syria, including the IS stronghold of Raqqa
The travel alert advises US citizens to "exercise vigilance when in public places or using transportation".
They are also advised to "be aware of immediate surroundings and avoid large crowds or crowded places".
"Authorities believe the likelihood of terror attacks will continue as members of ISIL/Da'esh [IS] return from Syria and Iraq," the state department said.
Belgian Prime Minister Charles Michel warned that the threat to his country remained "imminent and serious".
But he also said authorities were planning to reopen schools and the Brussels metro on Wednesday.
IS is believed to be behind the 13 November Paris attacks.
Co-ordinated assaults using guns and suicide vests were launched on several locations in the French capital.
Belgian prosecutors announced on Monday that a fourth suspect had been charged with terrorism offences related to the Paris attacks.
The unnamed man was one of 21 people detained in raids on Sunday and Monday. Seventeen have been released without charge.