Forces loyal to Muammar Gadaffi, the Libyan leader, are battling rebels in control of cities both close to the capital, Tripoli, and far away from it.
Reports said on Monday that fighter jets bombed an ammunition depot in the eastern city of Ajdabiya, while a resident of Az Zawiyah, 50km west of Tripoli, told the Associated Press news agency by telephone that fighting started on Monday evening and intensified after sundown when troops loyal to Gaddafi attacked the city from the west and east.
"We were able to repulse the attack. We damaged a tank with an RPG. The mercenaries fled after that," said the resident of Az Zawiyah, who spoke on condition of anonymity for fear of government reprisals.
He said Gaddafi called the city's influential tribal leader, Mohammed al-Maktouf, and warned him that if the rebels did not leave the main square by early Tuesday, they would be hit by fighter jets.
"We are expecting a major battle," the resident said, adding that the rebels killed eight soldiers and mercenaries on Monday.
Another resident of Az Zawiyah said he heard gunfire well into the night on the outskirts of town.
AP said its reporter saw a large, pro-Gaddafi force massed on the western edge of Az Zawiyah.
There were also about a dozen armoured vehicles along with tanks and jeeps mounted with anti-aircraft guns.
An officer said the troops were from the elite Khamis Brigade, named after one of Gaddafi's sons who commands it and said by US diplomats to be the best-equipped force in Libya.
The fighting came amid mounting international pressure on Gaddafi - already under sanctions over his handling of the turmoil - to end a crackdown on opponents pushing for his ouster.
Gaddafi, in power since 1969, remains defiant and has scoffed at calls to step down, saying foreign powers, including al-Qaeda and drug addicts, were behind the unrest.
The US, meanwhile, said it was moving warships and air forces closer to Libya and France said it would fly aid to the opposition-controlled eastern half of the country.
But Abdel Fattah Younes, Libya's former interior minister who has defected to the opposition, told Al Jazeera that welcoming "foreign troops" was "out of the question" although "touching down in Libya is acceptable only in the case of emergency".
"For example if any pilot was forced to eject, he will be hosted and protected by us," he said.
With government forces and rebels clashing in different parts of Libya, the security situation in and around Tripoli has made it too dangerous for international aid agencies to assess the need for medicine, food and other supplies there, according to the UN.
"The major concerns are Tripoli and the west where access is extremely difficult because of the security situation," Valerie Amos, the UN humanitarian chief, told Al Jazeera on Monday.
"There are reports that between 600 and 2,000 people have already been killed in Tripoli. We don't know the absolute accurate number because we haven't got people there who are able to do assessments ... we've seen some horrific pictures of what is happening and we really want to be able to go in to help people in the time of need."
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Amos also called on countries neighbouring Libya to keep their borders open so refugees can continue to flee.
As of Monday morning, an estimated 61,000 had fled into Egypt, 1,000 to Niger and 40,000 to Tunisia, according to the UN, which said there was concern about water and sanitation for the refugees.
Libya also borders Algeria, Niger, Chad and Sudan.
The International Committee of the Red Cross (ICRC) has also called for immediate and safe access to western Libya.
ICRC teams entered the eastern side of the country including the country's second city Benghazi over the weekend, and are now supporting local doctors with medical care. Two thousand people were wounded there, according to the agency.
A similar ICRC team including surgeons and supplies was waiting on the western border in Tunisia.
"Right now, the situation is far too unstable and insecure to enable much-needed help to enter western parts of the country," Yves Daccord, the ICRC director-general, said.
"Health and aid workers must be allowed to do their jobs safely. Patients must not be attacked, and ambulances and hospitals must not be misused. It's a matter of life and death."
Thousands of foreigners have been evacuated from Libya since the unrest began on February 17, with ships and aircraft sent by countries including China India, the US, Turkey and many other European countries.
Anti-government protests started in the country's second-largest city of Benghazi, which is now in the hands of the protesters, and have since spread to the west of the country.