The condition is that Liberian president Charles Taylor goes in to exile in Nigeria where he has been offered a safe haven.
A detachment of US troops and helicopters has already arrived in neighbouring Sierra Leone to support a team of American military experts operating in Liberia since last week.
After a meeting with United Nations Secretary-General Kofi Annan on Monday, Bush said he wanted to help bring peace to Liberia.
"Any commitment we have would be limited in size and limited in tenure," Bush said, adding that he was waiting for assessment reports from US teams in West Africa to take a final decision.
Bush added that for US troops to arrive in Monrovia, Liberian President Charles Taylor would have first to leave the country. Taylor has said he was willing to go into exile to Nigeria, but has not specified when.
Annan outlined a more detailed sequence for a Liberian operation, saying the Economic Community of West African States (ECOWAS) would initially send 1,000 to 1,500 troops to Monrovia. Then Taylor would leave. Simultaneously, US troops would arrive as well as more soldiers from West Africa.
Liberia has been in the grip of non-stop civil war for 14 years
Samuel Doe's ruthless dictatorship challenged in 1989 when Charles Taylor invaded from Ivory Coast
Seven years of ensuing mayhem costing 200,000 lives
Taylor has promised to leave country but wants war crimes indictment against him lifted
Washington is proposing to send soldiers to lead West African peacekeeping force
During this period, the United Nations would organise a peacekeeping force of "blue helmets".
More troops sought
“Once the situation is calm and stabilised, the US would leave and UN peacekeepers will carry on the operation," Annan said. None of the American peacekeepers would be under UN command.
Liberia's main rebel faction wants US troops to have "an overwhelming presence" on the ground in Liberia. It has suggested a US force should arrive before a West African peacekeeping force, a rebel spokesman said.
Kabineh Ja'neh, spokesman for Liberians United for Reconciliation and Democracy (LURD), was speaking by telephone from Accra, Ghana where he is taking part in peace talks.
"We would like to see an overwhelming presence of US troops on the ground. Whatever it takes to help us," Ja'neh said, without giving further details.
Liberia has been torn by almost non-stop conflict for 14 years, including a civil war in the 1990s in which 200,000 people were killed.