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The United States, which has long seen Saleh as a bulwark against a dynamic al Qaeda wing based in Yemen, has condemned the bloodshed and backed the right for peaceful protest, but has insisted only dialogue can end the political crisis.
Two soldiers and an officer were killed as clashes broke out in the northern al-Jawf province, which borders oil giant Saudi Arabia, Yemen's state news agency Saba said.
Fighting intensified after protesters stormed a municipal building. Security forces fired on them, wounding 10, but could not stop them seizing the building, a local official said.
In the central Maarib province, where several oil and gas fields of international companies are located, a man stabbed governor Naji Zayedi, critically wounding him as he and police tried to break up a crowd of thousands at a sit-in.
"Members of the opposition stabbed the governor and wounded three others as security tried to stop protesters from inciting chaos," a local official said.
OIL TRANSPORT BY TRUCKS SUSPENDED IN SOUTH
In the southern province of Shabwa, an official at Austrian oil firm OMV said the company had suspended its transports of crude by trucks from an oil field to the pumping station of a pipeline because of the unrest.
"The suspension is temporary and due to the current security instability," the official told Reuters, without saying how much oil was carried by trucks and what portion of it was for export.
Yemen is a small oil producer pumping about 300,000 barrels per day of crude.
As tensions in Yemen rose, three journalists and a researcher from Britain and the United States were abruptly deported on Monday. An airport official said they had all entered on tourist visas and were not entitled to work there.
Saleh has made many verbal concessions to the protesters, promising to step down in 2013 and offering a new constitution giving more powers to parliament, but he has steadfastly refused his critics' main demand that he leave office immediately.
Soldiers and armoured vehicles tried to cut off an area in the capital, where around 20,000 have held a sit-in for weeks.
"We're expecting an attack at any minute, but we're not leaving until the regime falls, " said protester Taha Qayed.
Crowds chanted: "Leave, leave you murderer."
Police fired in the air to try to break up tens of thousands of protesters in Taiz, 200 km (125 miles) south of the capital Sanaa. Three were hurt, but protesters continued demonstrating.
As demonstrations gather steam across the country, a string of Saleh's allies have recently defected to the protesters, who are frustrated by rampant corruption and soaring unemployment. Some 40 percent of the population live on $2 a day or less in Yemen, and a third face chronic hunger.
Activists said the former religious endowments minister of Yemen, sacked a day earlier, joined protests in Sanaa on Monday.
"We call on all ministers and all noble people to resign and join the revolution in Sanaa," leading activist Mohammed al-Sharfi told Reuters.
Thousands were also protesting in al-Hawta, the regional capital of southern Lahej province, residents said.
"Al-Hawta is in a state of paralysis. The opposition has called for a general strike to protest at the repression of demonstrators," a resident told Reuters by phone.
Popular revolts in Egypt and Tunisia have inspired this latest wave of unrest in Yemen, but the country was already seething with intermittent rebellions in the north and south