Clashes between the Hashid tribe and government forces have continued since Monday The tribal leader, Sheikh Sadeq al-Ahmar, has joined an uprising against President Saleh's rule.
On Sunday, the president refused to sign a deal to stand down.
One report early on Wednesday said forces loyal to Sheikh al-Ahmar had moved to take control of several public buildings.
They seized the state news agency Saba and the national airline building, while also trying to storm the interior ministry headquarters, AFP news agency reported.
'Don't take orders' But Mr Saleh remained defiant in a statement read by his spokesman on Wednesday.
Middle East unrest: Yemen 
- President Ali Abdullah Saleh in power since 1978
- Population 24.3m; land area 536,869 sq km
- The population has a median age of 17.9, and a literacy rate of 61%
- Youth unemployment is 15%
- Gross national income per head was $1,060 (£655) in 2009 (World Bank)
"I will not leave power and I will not leave Yemen," the spokesman, Ahmed al-Soufi, quoted the president as saying.
He dismissed fears that Yemen risked civil war, and that the country might turn into a failed state or an "al-Qaeda refuge."And he implicitly criticised Western efforts to mediate a transition, saying: "I don't take orders from outside."
He also said he was still prepared to sign a transition deal "within a national dialogue and a clear mechanism".
"No more concessions after today," he added.
Later on Wednesday, US President Barack Obama - in a joint press conference with British Prime Minister David Cameron in London - repeated his call for Mr Saleh to "move immediately on his commitment to transfer power".
Immunity The deal Mr Saleh has so far refused to sign called for him to step down within a month after 33 years in office and hand over power to a unity government.
It would also have given the president immunity from prosecution.
Mr Saleh has previously said he would only sign in the presence of opposition leaders.
Sheikh Ahmar, head of the powerful Hashid tribe, is a former supporter of the president. He joined the anti-government protests against Mr Saleh in March.
On Tuesday, his compound appeared to have been shelled as tribal leaders were trying to mediate a ceasefire there.
President Saleh has accused the sheikh of trying to provoke civil war, but the same accusation has been levelled against the president.
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