Key Yemeni General Ali Mohsen al-Ahmar, long close to President Ali Abdullah Saleh, says he is backing the protest movement against the regime.
Two other senior army commanders are also reported to have resigned.
President Saleh said he was "holding out" and the National Defence Council said it would block any "coup".
Tanks were deployed in the capital, Sanaa, apparently to defend key points including the presidential palace, defence ministry and central bank.
BBC security correspondent Frank Gardner says that one by one, the pillars of President Saleh's power are being knocked away.
The military commanders who announced their resignations are from President Saleh's Hashid tribe.
Sadiq al-Ahmar, head of the Hashid tribal federation, told al-Jazeera that it was time for Mr Saleh to make a "quiet exit".
One of the tribe's leaders said the Hashid were rallying behind Gen Ahmar as a possible replacement for President Saleh, the Associated Press reported.
Meanwhile, Yemen's foreign minister was sent to Saudi Arabia with a message from President Saleh to King Abdullah, the state news agency said. The contents of the message were not reported.
Gen Ahmar is the commanding officer of a division of the army which has sent units to a main square in the capital, Sanaa, where protests have taken place.
"The crisis is getting more complicated and it's pushing the country towards violence and civil war," the general - who commands an armoured infantry division - said in a statement broadcast by al-Jazeera television.
"According to what I'm feeling, and according to the feelings of my partner commanders and soldiers... I announce our support and our peaceful backing to the youth revolution. We are going to fulfil our duties in preserving security and stability."
Dozens of officers of various ranks lined up in central Sanaa to pledge their allegiance to the revolution.
The deputy speaker of parliament, the governor of the southern province of Aden, and a number of ambassadors were also reported to have resigned in protest against the violent suppression of anti-government demonstrations.
But President Saleh was defiant. "We're still here," he was quoted as saying. "The great majority of the Yemeni people are with security, stability and constitutional law.
"Those who are calling for chaos, violence, hate and sabotage are only a tiny minority."
A source close to Mr Saleh told the BBC that the president was not stepping down, and that he would call elections later this year.
The source claimed that if Mr Saleh left now, Yemen would descend into inter-tribal fighting within hours, and dismissed Gen Ahmar as someone who had never been close to the president.
The National Defence Council, which includes the military command and President Saleh, indicated in a statement they would oppose any effort to topple President Saleh.
"We will not allow under any circumstances an attempt at a coup against democracy and constitutional legitimacy, or violation of the security of the nation and citizens," the statement said, according to Reuters news agency.
"The armed forces will stay faithful to the oath they gave before God, the nation and political leadership under the brother President Ali Abdullah Saleh."
On Sunday, President Saleh fired his entire cabinet in apparent response to protests against his rule. He asked them to stay in place in a caretaker capacity.
The president has faced a number of resignations by ministers and officials since the killing of at least 45 people at an anti-government demonstration on Friday.
Gunmen in civilian clothes fired on the rally in the capital's central square, in what the opposition called a massacre.
The killings prompted tens of thousands of people to turn out at the funerals of the victims.
President Saleh declared a national state of emergency but denied his forces were behind the shooting.
Yemen is one of a number of countries in the region that have seen unrest since the presidents of Egypt and Tunisia were ousted in popular revolts.
The president has been in power for 32 years, facing a separatist movement in the south, a branch of al-Qaeda, and a periodic conflict with Shia tribes in the north.
He has said he will not seek another term in office in 2013, but has vowed to defend his regime "with every drop of blood".