"I will work with Congress to ramp up support for those in the Syrian opposition who offer the best alternative to terrorists and a brutal dictator," he said.
His remarks were immediately hailed by the Syrian Opposition Coalition, which said in a statement it "appreciates American support to the Syrian people in their struggle against the Assad regime."
Administration officials said the proposed mission would be aligned with, but not necessarily part of a new $5 billion counterterrorism initiative that Obama announced in his speech.
The officials said they would seek congressional authorization for the program because it might require invoking the War Powers Act.
The Senate Armed Services Committee last week passed a bill that authorizes the Defense Department to provide training and equipment elements of the Syrian opposition that have been screened. It is unclear when the bill may be considered by the full Senate or the House.
Under the planned initiative, the U.S. would send a limited number of American troops to Jordan to be part of a regional training mission that would instruct carefully screened members of the Free Syrian Army on weapons handling and tactics, officials said.
The officials spoke on condition of anonymity because they were not authorized to discuss administration deliberations by name.
In addition to the counterterrorism aspect, the State Department, the Pentagon and U.S. intelligence agencies, along with many in Congress who back the move, have concluded Assad will not budge without a change in the military situation in Syria.
The U.S. has covert support operations in place for the Syrian opposition and has spent $287 million so far in nonlethal aid on the civil war, now in its fourth year with a death toll surpassing 160,000, according to estimates.
Rebel commanders for three years have asked the U.S. for lethal assistance as they've seen gains wiped out one after another. The U.S. has been reluctant to move to that kind of aid for fear weapons could end up in the hands of extremist rebels who might then turn on neighboring Israel or against U.S. interests.
The proposed mission would be coordinated by the U.S. but involve many of the regional players active in assisting the rebels, including Turkey, Jordan, Saudi Arabia, Kuwait and the United Arab Emirates, the officials said.
Saudi cooperation is critical and has been a main topic of conversation in recent weeks between the U.S. and the kingdom, including Obama and Saudi King Abdullah, the officials said.
The proposal has evolved in intense, high-level discussions between the United States and Jordan, which over the weekend expelled the Syrian ambassador as part of what is planned to be an escalation in the effort to isolate Assad.
Assad is running for re-election in a June vote that the U.S. and its allies have condemned as a farce.
Jordan's King Abdullah II was in Washington last week and met with Secretary of State John Kerry. Defense Secretary Chuck Hagel made a stop in Jordan this month during a Middle East trip.
The U.S. has roughly 1,500 military troops in Jordan, in addition to the approximately 6,000 that recently arrived there for a limited time to participate in the annual Eager Lion military exercise.
Eager Lion 2014 includes members of the Army, Navy, Air Force and Marines, as well as U.S. ships and aircraft. The exercise started this past weekend.
Last year, after Eager Lion 2013 finished, the U.S. left a detachment of F-16 fighter jets and a Patriot missile battery there and about 1,000 personnel associated with the aircraft and the missile system. There also is a staff of about 400 U.S. military in Jordan and there were troops there to assist the Jordanians with chemical weapons training.
Small teams of U.S. special operations forces also have rotated in and out of the country conducting exercises with Jordanian and Iraqi commandos. The last session was in April and another is scheduled for June.
AP White House Correspondent Julie Pace contributed to this report.