"We promise that anywhere the girls are, we will surely get them out," Jonathan said in a live broadcast on radio and television.
"This is a trying time for this country ... it is painful," he said, and pleaded for the co-operation of parents, guardians and the local communities in the rescue efforts.
Besides the US, Jonathan said Nigeria had also approached other world powers, including France, Britain and China, for help on security issues. His Government is also seeking the co-operation of neighbouring countries - Cameroon, Chad, Niger and Benin - in its efforts to rescue the girls.
The British Government said it was ready to give "practical assistance" as Nigerian troops were reported to be massing around a forest where at least 223 teenage girls were thought to have been taken after a night raid on their dormitories.
A spokesman for the British Foreign Office said: "If we can provide practical assistance we stand ready to do so. We are discussing how we might help with various parts of the Nigerian Government and security services."
Officials declined to say whether British help would include Special Forces. British troops have operated in Nigeria before, including a failed attempt in 2012 by Special Boat Service commandos to rescue the British hostage Chris McManus.
Boko Haram, whose name means "Western education is forbidden", is a violent jihadist group that has extended its sway in parts of Muslim northern Nigeria dramatically in the past two years. The mass abduction is one of the group's most shocking attacks in an uprising that is thought to have killed 1500 people this year alone.
Officials estimated at least 276 girls were taken captive in the Sambisa forest, though 53 managed to escape.
Two who escaped told a Nigerian newspaper that they had leaped from trucks as they were being driven away by their captors.
Thabita Walse told the Sunday Punch: "Our vehicle developed a problem and they were forced to stop. I took the opportunity with some girls to run into a dark bush."
Amina Sawok added: "I have heard a lot about Boko Haram, the bad things they do and how they have killed many people in the state.
"I was afraid and I became desperate. I felt getting to their camp could be dangerous for me, and it would be better if I escaped. That gave me the courage to jump out. Immediately one of us jumped out, the rest of us just started following her."
Four battalions of troops were yesterday stationed around the Sambisa forest, a former game reserve. Soldiers were backed by fighter aircraft and helicopter gunships.
- AFP