Troops loyal to President Ali Abdullah Saleh clashed with those supporting Gen Ali Mohsen al-Ahmar, who has defected to the opposition.
In the southern city of Aden, soldiers opened fire as protesters threw stones and set up roadblocks to stop troops patrolling the streets.
One person was killed and several others wounded, reports say.
Tens of thousands of people are marching in cities across the country, as protesters keep up weeks of pressure aimed at forcing President Saleh out of power after 32 years in office.'Worrying development'
The clash in Sanaa between rival security forces happened early on Wednesday morning at a checkpoint run by the first army division, which supports the opposition.
The rival sides exchanged fire with machine-guns and rocket-propelled grenades after the pro-opposition soldiers stopped a car carrying pro-government security personnel, who reportedly refused to be searched.This is a particularly worrying incident as Yemen's capital is guarded by two rival military units, and any confrontation between them could be very difficult to contain, says a BBC correspondent in Sanaa.
More than 100 people have been killed since the start of the protests on 11 February, which were inspired by the popular uprisings that toppled long-time rulers in Tunisia and Egypt.
In addition to democratic and economic reforms, the protesters want to see legal action against Mr Saleh and his sons, who occupy key security and political posts.
On Monday, opposition groups rejected outright a proposal by Gulf Arab countries for Mr Saleh to transfer power to his deputy in exchange for immunity from prosecution.
They now say they will hold talks with Gulf ambassadors to see if a timetable can be agreed and other details ironed out.
Even before the mass protests, Mr Saleh was struggling to quell a separatist rebellion in the south and a Shia Muslim insurgency in the north.
Analysts fear the violence could give the Arabian Peninsula branch of al-Qaeda more room to operate.
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