"I am waiting to talk to my mother by phone. I want to tell her that I love her and that she has been missed."
Sarkozy praised the "successful military operation" by the Colombian military that freed Betancourt, and called on the Revolutionary Armed Forces of Colombia (Farc), which had taken her captive to end their "absurd" struggle.
George Bush, the US president, also welcomed Betancourt's release.
"This is positive news but we should not forget about the other hundreds who continue to be held across Colombia"
Amnesty International, a human rights group
"President Bush congratulated President Uribe, telling him he is a 'strong leader'," after the military operation, said Gordon Johndroe, a White House spokesman.
Relatives of the three US hostages - Marc Gonsalves, Thomas Howes and Keith Stansell - thanked Colombian soldiers for their rescue, their spokesman said.
"The families express their gratitude to the soldiers and the Colombian intelligence forces, who risked their lives in this daring operation," said Stephen Donehoo.
Ban Ki-moon, the UN secretary general, "warmly welcomes the rescue" of the hostages and called on the rebels "to immediately and unconditionally release the remaining hostages", his spokeswoman said.
Amnesty International, the human rights group, also drew attention to the captives still being held by the group.
"This is positive news but we should not forget about the other hundreds who continue to be held across Colombia. We urge the Farc to release them immediately and unconditionally."
Betancourt was the most high-profile of about 700 people believed to have been taken captive by the Farc, Latin America's oldest armed rebel group.
Venezuela, which has negotiated hostage releases with the Farc in the past, joined the "jubilation" celebrating the release on Wednesday, a government-issued statement said.
"Our government reiterates the request ... to liberate the captives [Farc] still has in its power," it said.
According to state-run channel VTV, Hugo Chavez, Venezuela's president, called Uribe to congratulate him on the liberation.
In January and February, the Farc delivered six hostages to Chavez representatives, who traveled to secret locations in the Colombian jungle to get them.