The alert level remained unchanged, Swiss authorities said, but various events planned over the weekend will go on.
The U.S. Embassy warned Americans
to "maintain a high level of vigilance."
The Swiss alert came after a tip from U.S. intelligence officials, who told their Swiss counterparts that they had intercepted communications among extremists discussing the idea of attacking Geneva, as well as Chicago and Toronto, a source close to the investigation told CNN.
Authorities were looking for at least two other people with indirect links to suspects in the November 13 Paris terror attacks.
"We have gone from a vague threat to a precise threat," Emmanuelle Lo Verso, head of communications at the Geneva Department of Security, told CNN. She would not comment further.
Whatever the nature of that threat, it was likely more well developed than any possible danger for Chicago or Toronto, said CNN national security analyst Juliette Kayyem.
Kayyem said she suspects that "the intelligence about Geneva was stronger, more specific than it was about the other cities because you're simply not hearing about that kind of reaction from either Toronto or Chicago at this stage."
Geneva police Chief Monica Bonfanti told radio broadcaster RTS that there is "the possibility of the presence of an Islamic State (ISIS) terror cell in Geneva." Bonfanti said police were searching for terror suspects, but wouldn't comment on the number of people involved in the hunt.
In Switzerland, authorities raised the terror alert level and deployed more armed police officers on the streets.
At the United Nations complex in Geneva
, security officials stood guard with heavier weapons than usual, spokesman Rheal LeBlanc told CNN.
A security scare shut down Geneva's airport for about 20 minutes as authorities examined two suspicious objects. One was a piece of forgotten luggage, an airport spokesman told CNN. The other item was detonated in a controlled explosion.
Intelligence information about the people involved in the Paris attacks has come from several nations, one of them Morocco. There was terror arrests in that country Friday; officials said nine ISIS members were arrested. Authorities said they had dismantled a dangerous terror cell, but gave no details about the group's plans, Morocco state news agency Maghreb Arabe Presse reported.