CAIRO — Yemeni President Ali Abdullah Saleh’s ruling coalition continued to crumble Monday as three top military commanders joined the opposition.

Maj. Gen. Ali Muhsin Saleh cited the killing of more than 50 civilians by government loyalists in a statement recorded for the al-Jazeera television network. He has family ties to the president and is chief of the military’s powerful first brigade.

“”The state, represented by the president, is totally responsible for the blood that was shed,”” he said, noting that his defection was “”an answer to the developments in the streets.””

The other resignations came from the general’s prominent subordinates, Brigadiers Mohammed Ali Mohsen and Hameed Qusaibi, who share responsibility for Yemen’s war-torn northwest. The army has battled there with Shiite rebels for almost a decade.

Meanwhile, protesters outside Sana University, near the center of the capital city, reported that some loyalist soldiers have begun to withdraw from the demonstration area. They were replaced by soldiers under the command of Muhsin Saleh’s men, a development the crowd met with jubilation.

“”This is our most important victory so far,”” said Issam Badr, a 19-year-old pharmacist who has attended the demonstrations since they began early last month.

“”No more thugs can kill us with impunity,”” he said. “”Everybody here welcomes the first brigade and salutes its soldiers for their patriotism and for helping the nation at this critical time.””

The military defections follow a flurry of resignations in recent days that included the president’s representative to the United Nations and key Cabinet ministers. The president sacked his entire Cabinet late Sunday in an apparent effort to preempt further resignations.

Despite the president’s mounting troubles, however, his security forces were visible throughout the city Monday and controlled major intersections and government buildings.

Saleh, a strongman who has ruled for 33 years, is considered a master political tactician, and few longtime observers were ready to predict an imminent departure.

“”The government is experienced in managing divisions, however large, to its benefit,”” said Abdul Rahman Marwani, a political analyst in Yemen.