The embassy issued a “security message” on its website on Thursday after Geneva and Swiss federal authorities announced they were conducting a criminal investigation into the “possible planning of a terrorist event”.
Both federal and cantonal authorities have been short on specifics about the terrorist threat “for tactical reasons” but they say they are looking for suspected jihadists.
Swiss media have reported that at least four and possibly six people are being sought by police in connection with the investigation that has put law enforcement officers on high alert.
The cities of Geneva, Chicago and Toronto were listed as possible targets in a police document cited by local reports.
Guards with submachine guns have been posted outside the entrance to the United Nations and other international organizations in Geneva, and armed police were visible at the airport and main train station.
“In this time of elevated threat, the US Embassy in Bern reminds US citizens to review personal security plans, remain aware of surroundings at all times and monitor local news stations for updates,” the message on its website said.
It also recommended that Americans travelling to or residing in Switzerland enroll in the US Department of State's “smart traveller enrolment programme”.
The programme is designed to provide the latest security updates and “makes it easier for the nearest US embassy or consulate to contact you in an emergency”.
The Canadian federal government said it is "vigilant" and "alert" to terrorist threats after warnings of possible plots against its major cities linked to the Islamic State extremist group, public safety minister Ralph Goodale said on Thursday.
"To this moment there is nothing new or different that would affect the security situation in
Canada,” Goodale told reporters outside parliament in Ottawa.
“There is no change in the status of the alerts (in Canada),” he said.
"There is no new information reported to me that would change the circumstances. “If there is something new we would obviously let Canadians know immediately and we will take the appropriate steps.”
The UK Embassy in Bern on its website advised British citizens to “follow the instructions of Swiss security authorities . . . who have confirmed an ongoing police operation in the Geneva area.”
It added that Geneva police had “raised its level of vigilance but Swiss authorities have not otherwise changed the overall public security status in Switzerland”.