"He will continue to employ heavier and heavier weapons on his people," Mattis said. "I think it will get worse before it gets better."
Mattis predicted that al-Assad will retain power "for some time."
Also Tuesday, preliminary discussions began among the five permanent members of the Security Council plus Morocco "about whether there is any possibility of reaching agreement around a potential text that would demand an end to the violence in Syria and demand immediate humanitarian access," said Susan Rice, U.S. ambassador to the world body. "These discussions are just beginning and will continue. If and when it seems there is a basis for a meaningful and viable text, we will propose one to the full Security Council."
Western diplomats said the goal is to bring the Russians and Chinese into the fold by creating a less harsh version of the last resolution, which the two countries vetoed, that would emphasize the humanitarian situation. They said they want the Russians and Chinese to join the call for a "permissive environment" for humanitarian access.
However, the United States and its allies insist the resolution puts the onus on the regime to stop the violence and will not give up on that issue. This is a nonstarter for the Russians and Chinese, who want any resolution to reflect that armed opposition rebels also bear responsibility.
On Monday, Russian Deputy Foreign Minister Gennady Gatilov posted a message on his Twitter page saying the latest version of a draft resolution doesn't pass his muster.
Turkish Prime Minister Recep Tayyip Erdogan called Tuesday for the opening of a humanitarian aid corridor to Syria. In his televised weekly party parliamentary group meeting, he also called for the implementation of an Arab League plan that calls for al-Assad to step down and demands an immediate end to human rights violations and attacks against civilians. The U.N. General Assembly passed a nonbinding resolution last month endorsing the plan.
U.S. Sen. John McCain, R-Arizona, called Monday for the United States to lead an international effort to protect the Syrian population via piloted airstrikes on regime forces.
The Syrian American Council, an organization for Syrians living in the United States, issued a statement supporting McCain's call. SAC Chairman Mahmoud Khattab said airstrikes would amplify the capabilities of the Free Syria Army, a group primarily made up of Syrian army defectors fighting against the regime.
"It took Assad's well-equipped army 27 days of full-scale assault on the Baba Amr district of Homs, which indicates the effectiveness of the FSA and the exhaustion of the Syrian Army," Khattab said in a statement. "Providing military support for the army defectors will further weaken Assad's forces and help topple the regime."
But U.S. Defense Secretary Leon Panetta was noncommittal.
"The secretary is interested in exploring options that could help end the brutal violence in Syria, but he also recognizes that this is an extremely complex crisis," a senior Pentagon official said. "Intervention at this time could very well exacerbate problems inside the country."
House Speaker John Boehner said Tuesday that he doesn't share McCain's view. "Until there's clear direction on what's happening there, involving ourselves at this point in time would be premature," he said.
While officials in the West and elsewhere discussed the crisis from afar, more carnage mounted across Syria.
The Syrian regime consistently has blamed the violence on "armed terrorist groups" and portrayed its forces as trying to protect the public interest and security. The Syrian government says that more than 2,000 security personnel have been killed in the violence, including 12 "martyrs" it said were buried Monday.
CNN cannot independently confirm reports across Syria because the government has severely restricted the access of international journalists. But the vast majority of reports out of Syria indicate al-Assad's forces are slaughtering civilians in opposition hotbeds in an attempt to wipe out dissidents.
The United Nations says that at least 7,500 people have died in the crackdown, while opposition activists put the toll at more than 9,000.
For months, diplomatic efforts have failed to stop the bloodshed. But international leaders haven't given up on diplomacy.
Valerie Amos, U.N. under-secretary-general for humanitarian affairs and emergency relief coordinator, is slated to arrive Wednesday in Damascus for a two-day visit. "My aim is to urge all parties to allow unhindered access for humanitarian relief workers so that they can evacuate the wounded and deliver essential supplies," Amos said in a statement.
She will meet with Foreign Minister Walid al-Moallem and "will pay visits to some areas in Syria," SANA reported.