Assad is president of the Arab nation.
The senators also asked Dempsey whether the U.S. military has the ability to significantly reduce Syria's air power, ballistic missiles and heavy artillery, and whether taking that step would shift the balance of power in the civil war.
Col. Edward Thomas, a spokesman for Dempsey, said the military leader would respond to the request.
At the hearing Thursday, McCain asked Dempsey to provide his personal opinion on which approach in Syria carries greater risk for U.S. national security interests: continued limited action on the part of Washington, or more significant steps such as establishment of a no-fly zone and arming rebel forces with the weapons they need to stem the advance of Assad's forces.
Dempsey said he has provided President Barack Obama with options for the use of U.S. military force in Syria, but he declined to detail those choices.
"It would be inappropriate for me to try to influence the decision with me rendering an opinion in public about what kind of force we should use," Dempsey said.
Dempsey added that the question of whether to support the opposition forces in Syria "with direct kinetic strikes ... is a decision for our elected officials, not for the senior military leader of the nation."
The use of kinetic strikes, a military term that typically refers to missiles and bombs, "is under deliberation inside of our agencies of government," he said.
Dempsey's response, McCain said, contradicted his commitment to provide the committee with his personal views, even if those opinions differ from the administration in power.
In releasing the letter, the senators said they expected answers "as soon as possible in order to move forward promptly with the confirmation."
The letter also seeks Dempsey's assessment of the Afghan National Security Forces and the risks associated with pulling U.S. forces out of Afghanistan.
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Associated Press writer Richard Lardner contributed to this report.