The situation in Syria is "spinning out of control," U.S. Defense Secretary Leon Panetta said on Wednesday, adding that President Bashar Assad's government would be held responsible if it failed to safeguard its chemical weapons sites.

Syria's defense minister and Assad's brother-in-law were killed in a Damascus suicide bomb attack carried out by a bodyguard on Wednesday, the most serious blow to the president's high command in the country's 16-month-old rebellion.

"This is a situation that is rapidly spinning out of control," Panetta said, adding that the international community needed to "bring maximum pressure on President Bashar Assad to do what's right, to step down and allow for that peaceful transition."

Panetta's comments to a Pentagon news conference followed closed door talks with his British counterpart, Defense Secretary Philip Hammond. Hammond, speaking alongside Panetta, said he believed the situation in Syria was deteriorating and "becoming more and more unpredictable."

The Damascus attack, Hammond said, showed the country's growing instability as the violence gets closer to the heart of the government.

"I think what we're seeing is an opposition which is emboldened, clearly an opposition which has access increasingly to weaponry, probably some fragmentation around the edges of the regime as well," he told reporters.

The Assad government appears to be quietly shifting some chemical weapons from storage sites, Western and Israeli officials have said, but it is not clear whether the operation is merely a security precaution amid Syria's escalating internal conflict.

The Syrian government denies carrying out the operation. Syrian's undeclared stockpile - believed to be the largest of its kind in the Middle East - reportedly includes sarin nerve agent, mustard gas and cyanide.

"We've made very clear to them that they have a responsibility to safeguard their chemical sites and that we will hold them responsible should anything happen with regards to those sites," Panetta said, adding that the United States was working closely with its allies on the issue.

Hammond said it was important to marshal the support of those countries that still give tacit support to the regime, in what appeared to be a veiled reference to Russia and China.

"So our diplomacy has to focus on getting those who have the greatest influence with the regime to ensure that it acts responsibly in relations to chemical weapons," Hammond said.