The measure is expected to reach the Senate floor next week, although the timing for a vote is uncertain. Sen. Rand Paul, a Kentucky conservative with strong tea party ties, has threatened a filibuster.
The House also is reviewing Obama's request, but its timetable is even less certain.
The administration blames Assad for a chemical weapons attack that took place on Aug. 21 and says more than 1,400 civilians died, including at least 400 children. Other casualty estimates are lower, and the Syrian government denies responsibility, contending rebels fighting to topple the government were to blame.
The Senate panel's vote marked the first formal response in Congress, four days after Obama unexpectedly put off an anticipated cruise missile strike against Syria last weekend and instead asked lawmakers to unite behind such a plan.
The president was in Sweden after a day of diplomacy when the vote occurred. At a news conference earlier, he said, "I always preserve the right and responsibility to act on behalf of America's national security." In a challenge to lawmakers back home, he said Congress' credibility was on the line, not his own, despite saying a year ago that the use of chemical weapons would cross a "red line."
Secretary of State John Kerry said he believes Obama will address the nation on Syria in the next few days. The president returns home from overseas Friday night.
Obama's request also received its first hearing in the House during the day, and Kerry responded heatedly when Rep. Jeff Duncan, R-S.C., said that Kerry, Obama and Vice President Joseph Biden all had advocated for caution in past conflicts. "Is the power of the executive branch so intoxicating that you have abandoned past caution in favor of pulling the trigger on a military response so quickly?" Duncan asked.
Kerry, who fought in Vietnam in the 1960s and voted to authorize the war against Iraq a decade ago, shot back angrily: "I volunteered to fight for my country, and that wasn't a cautious thing to do when I did it." When Duncan interrupted, the secretary of state said," I'm going to finish, congressman," and cited his support as senator for past U.S. military action in Panama and elsewhere.
Asked during the hearing about international support for Obama's threatened military strike, Kerry said the Arab League has offered to pay the cost of any U.S. military action. He was not specific but said the offers have been "quite significant, very significant."
The Senate committee's vote capped a hectic few days in which lawmakers first narrowed the scope of Obama's request — limiting it to 90 days and banning combat operations on the ground — and then widened it.
Sen. John McCain, R-Ariz., a proponent of aggressive U.S. military action in Syria, joined forces with Democratic Sen. Chris Coons of Delaware to add a provision calling for "decisive changes to the present military balance of power on the ground in Syria."
At their urging, the measure was also changed to state that the policy of the United States is "to change the momentum on the battlefield in Syria so as to create favorable conditions for a negotiated settlement that ends the conflict and leads to a democratic government in Syria." McCain, who has long accused Obama of timidity in Syria, argued that Assad will be willing to participate in diplomatic negotiations only if he believes he is going to lose the civil war he has been fighting for over two years.
The changes were enough to attract bipartisan support, but political fault lines were evident inside each party on a military action that polls show a war-weary public opposes.
Seven Democrats and three Republicans supported the measure, while two Democrats and five Republicans opposed. Among Republicans, opposition came from lawmakers with the closest ties to tea party activists, including Paul and Florida Sen. Marco Rubio, both presidential aspirants.
Among Democrats, Kerry's replacement in the Senate, Sen. Ed Markey, D-Mass., voted "present" after expressing misgivings.
In his comments in Sweden, the president sought to shift the onus for responding to Assad to Congress and the world at large. "I didn't set a red line. The world set a red line" with a treaty banning the use of chemical weapons. He added that "Congress set a red line" when it passed legislation a decade ago demanding Syria stop production of weapons of mass destruction.
His comments drew a disbelieving response from one Republican back home.
"He needs to go back and read his quote," Sen. Saxby Chambliss of Georgia said, referring to a comment the president made slightly more than a year ago. On Aug. 20, 2012, Obama said, "We have been very clear to the Assad regime, but also to other players on the ground, that a red line for us is we start seeing a whole bunch of chemical weapons moving around or being utilized. ... "That would change my calculus" about military action, he added at the time.
Elsewhere on Wednesday:
— In Syria, al-Qaida-linked rebels were said to have launched an assault on a government-held Christian mountain village in the densely populated western part of the country, and there was new fighting near Damascus as well.
— In Rome, Pope Francis underscored Vatican opposition to threatened military strikes against Syria, urging Catholics and non-Catholics alike to take part in a day of fasting and prayer for peace on Saturday. He has called for a negotiated settlement in Syria and also has condemned the use of chemical weapons.
— In France, Prime Minister Jean-Marc Ayrault told parliament that failure to take action would allow Assad to launch more chemical attacks.
In Washington, Kerry said Assad had used chemical weapons 11 times, including once last spring. At that time, he said, Obama did not have a "compelling" enough case to push for a U.S. military response.
As for the most recent chemical weapons attack, Kerry declared that "only the most willful desire to avoid reality can assert that this did not occur as described or that the regime did not do it. It did happen - and the Assad regime did do it."
Few if any members of Congress dispute the administration's claim that Assad was responsible for the attack, and lawmakers in both parties appear far more focused on determining how they should respond.
Gaveling the House committee hearing to order, Rep. Ed Royce, R-Calif., said that while it would be important to deter the use of chemical weapons by Assad and others, there remained many unanswered questions, including what the U.S. would do if Assad retaliated.
"The administration's Syria policy doesn't build confidence," he said.
In a letter to her rank and file, Democratic Leader Nancy Pelosi of California said she had received suggestions for legislation in the House "to add language to prevent boots on the ground, to tie the authorization more closely to the use of chemical weapons and to address concerns about an open-ended timetable."