"I think [it] has been made very clear ... if any action would be taken against Syria, it would be an international collaboration," Hagel said.
Russian Deputy Minister of Defense Anatoly Antonov backed Hagel's call for international support for any coming military action in Syria during Thursday's ASEAN press briefing.
Moscow "is consulting with all parties concerned" regarding possible American military strikes in Syria, Antonov said.
Russia, along with Iran, is the biggest international supporters of embattled Syrian President Bashar Assad.
"I am sure that we have to go along with the international law, and ... we have excellent institutions and mechanisms" at the United Nations and elsewhere to ensure an international consensus can be built around any future operation in Syria," according to Antonov.
"I'm sure that there is opportunity to find solution," he added.
Hagel and Antonov's comments come as Obama administration officials are weighing whether to begin military strikes against Assad's forces in Syria.
The strikes being considered by the White House are in retaliation for alleged chemical weapons attacks by Syrian forces against anti-government rebels in the country.
On Thursday, the Pentagon ordered a fifth Arleigh Burke-class Navy destroyer into the coastal waters off Syria.
U.S. commanders have already stationed four other Navy warships in the area, armed with long-range Tomahawk cruise missiles, in preparation for possible military action.
London has also begun moving fighter jets and cargo aircraft to the United Kingdom's massive air base in Cyprus, off the Syrian coast, to support the expected American offensive.
Prior to Thursday's statements Hagel told reporters that U.S. military leaders were "ready to go" if the order to begin missile strikes was handed down by Obama.
The White House is actively pursuing avenues outside the U.N. to provide legal justification for military strikes in Syria.
Administration officials are looking to bypass U.N. Security Council approval for any military action, due to the guaranteed opposition from Russia, which holds a seat on the international governing body.