The Syrian military continued its bombardment of rebel strongholds Wednesday, amid suggestions from U.S. Secretary of State Hillary Clinton that President Bashar al-Assad could be branded a war criminal.

According to Reuters, a senior Tunisian official agreed to offer Assad asylum if he promised to step down, offering some hope of a peaceful end to the 11-month-old struggle against the Syrian autocrat's rule.

Clinton's comments echo those of Navi Pillay, the United Nations' top human-rights official, who told a meeting of the Human Rights Council on Tuesday that Syria should be referred to the U.N.-backed International Criminal Court.

There would be an argument to be made that he would fit into that category, Clinton told a U.S. Senate committee hearing Tuesday, responding to a question from Sen. Lindsey Graham, a Republican from South Carolina, as to whether Assad could be called a war criminal.

But the secretary added that using such labels limit options to persuade leaders to step down from power, Reuters reported.

Clinton was also asked whether she thought Assad was on his way out eventually. I do, she said. I just don't know how to define 'eventually.'

Despite the diplomatic pressure, reports Wednesday indicated Syrian government troops were pushing further into the besieged city of Homs, a center of resistance against Assad's rule.

According to the Associated Press, a senior Syrian official confirmed the military was advancing on Baba Amro, a central district in Homs, with the official adding that the area would be cleaned within hours, suggesting troops were confident of retaking the city from opposition groups.

It was unclear if a ground offensive was underway, but concerns have been raised about the fate of three foreign journalists trapped in Homs.

According to Syrian activists, 26 more people were killed Tuesday in Baba Amro, adding to the 102 estimated to have died in earlier fighting in the city.