The BBC correspondent in Sanaa says the area has been blocked off by army trucks, and single gunshots echo through the city.
Doctors say at least a dozen people have gunshot wounds, and others were treated for the effects of tear gas.
The country has seen weeks of protests against President Ali Abdullah Saleh.
President Saleh earlier recalled his ambassador to Qatar after dismissing a proposal by the Gulf states for him to step down.
Our correspondent says the sounds of single gunshots are consistent with the accounts from some protesters inside the area who say snipers are shooting at them from rooftops.
On Thursday, Qatari Prime Minister Sheikh Hamad Bin Jassem Al Thani said the six-nation Gulf Co-operation Council (GCC) hoped "to reach a deal with the Yemeni president to step down". In return, he and his family would be granted immunity from prosecution.
But Mr Saleh said: "Our power comes from the power of our great people, not from Qatar, not from anyone else. This is blatant interference in Yemeni affairs."
He added: "We reject any coup against democracy, the constitution and our freedom... We reject this belligerent intervention."
A BBC correspondent says Mr Saleh's speech was brief but potentially very damaging to any prospect of resolving this crisis peacefully.
Diplomats and government sources in Sanaa say that the president's family members, many of whom hold powerful positions, are putting a lot of pressure on him to stay, our correspondent adds.
More than 120 people have been killed since Yemenis began calling for the removal of President Saleh after 32 years in power, inspired by the popular uprisings in Tunisia and Egypt.
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