But a rebel spokesman said Muammar Gaddafi's forces were still shelling two cities.
The United States said a ceasefire announcement was insufficient, calling on the regime to pull back from eastern Libya where the rebels found themselves facing rockets, artillery, tanks, warplanes.
Eastern Libya has the majority of Libya's oil reserves - the largest in Africa.
Oil prices slid after the cease-fire announcement, plunging about 2.50 dollars in the first 15 minutes of New York trading. By midday, they stood at 101 dollars.
Mustafa Gheriani, a spokesman for the rebels, said attacks continued well past the announcement, which came after a fierce government attack on Misrata, the last rebel-held city in the western half of the country. A doctor said at least six people died.
"He's bombing Misrata and Adjadbiya from 7 am this morning until now. How can you trust him?" Gheriani said.
The UN Security Council resolution, which passed late on Thursday, set the stage for air strikes, a no-fly zone and other military measures short of a ground invasion.
Britain announced that it would send fighter jets, Italy offered the use of its bases, and France made plans to deploy planes.
The US, which has an array of naval and air forces in the region, had yet to announce its role.
With the international community mobilising, Libyan Foreign Minister Moussa Koussa said the government would cease fire in line with the resolution, although he criticised the authorisation of international military action, calling it a violation of Libya's sovereignty.
"The government is opening channels for true, serious dialogue with all parties," he said during a news conference in Tripoli, the capital. He took no questions.
In Washington, Secretary of State Hillary Clinton said that the first goal of international action was to end the violence in Libya and protect civilians. She said government forces, which have advanced along the Mediterranean coast in recent days, must pull "a significant distance away from the east".
A large crowd in the Benghazi, the city where the uprising started on February 15, watched the UN vote on an outdoor TV projection and burst into cheers, with green and red fireworks exploding overhead. In Tobruk, another eastern city, happy Libyans fired weapons in the air to celebrate.
"We think Gaddafi's forces will not advance against us. Our morale is very high now. I think we have the upper hand," said Col Salah Osman, a former army officer who defected to the rebel side. He was at a checkpoint near the eastern town of Sultan.
Western powers faced pressure to act quickly as Gaddafi's forces gained momentum.
"We're extremely worried about reprisals by pro-government forces and security agents in Libya. No one knows what's going on in the towns recaptured, and what's going on in prisons and other state security premises across the country," said Rupert Colville, spokesman for the UN Office of the High Commissioner for Human Rights.
"We are very concerned that the government could resort to collective punishment and we have no illusions about what this regime is capable of."
More than 300,000 people have fled Libya since fighting began, the UN said, and the exodus shows no signs of slowing.
In an interview with Portuguese television broadcast just before the UN vote, Gaddafi pledged to respond harshly to UN-sponsored attacks. "If the world is crazy," he said, "we will be crazy, too."
The Libyan government closed its airspace today, according to Europe's air traffic control agency, Eurocontrol.
Government tanks rolled into Misrata, 125 miles (200 kms) south-east of Tripoli, early today, shelling houses, hospitals and a mosque for several hours before pulling back to the city's outskirts, witnesses said.
At least six people were killed, raising the total death toll in two days of fighting to nine, a local doctor said.
Misrata is the rebels' last western base after Gaddafi recaptured a string of other cities that fell to the opposition early. Its fall would leave the country largely divided, with the rebels bottled up in the east near the border with Egypt.
The city has been under a punishing blockade that has prevented aid ships from delivering medicine and other supplies, the doctor said.
"They haven't stopped shelling us for a week - we sleep to shelling, and wake up to shelling. They are targeting houses and hospitals," he said, adding the hospital had been overwhelmed.
"We have had to perform surgeries in the hallways using the light from our cell phones to see what we're doing. We are also using some clinics around the town, some only have 60 beds, which isn't enough," he said.
Another doctor claimed Gaddafi's forces had surrounded some neighbourhoods and were shooting at people who ventured outside. "Militias used two ambulances to jump out of and shoot at innocent people indiscriminately," he said.
Gaddafi troops encircled the city of Ajdabiya but also had some troops positioned beyond it toward Benghazi, the second largest Libyan city, with a population of about 700,000.
Libya's unrest began in Benghazi and spread east to Tripoli. Like others in the Mideast, the uprising started with popular demonstrations against Gaddafi, rejecting his 41 years of despotic and often brutal rule.
The tone quickly changed after Gaddafi's security in Tripoli forcefully put down the gatherings there.
Soon rebel forces began arming themselves, quickly taking control of the country's east centred on Benghazi. Some Libyan army units joined the rebels, providing them with some firepower.
There are no reliable death tolls. Rebels say more than 1,000 people have been killed in a month of fighting, while Gaddafi claims the toll is only 150.
Libya's deputy foreign minister, Khaled Kaim, denied government forces had violated the cease-fire.
He invited four nations to send observers to monitor Libyan compliance: Germany, China, Turkey and Malta.
"The cease-fire for us means no military operations whatsoever, big or small," he told reporters in Tripoli.
He said military forces were positioned outside Benghazi but that the government had no intention of sending them into the city.
He also invited the UN chief to send a fact-finding mission and asserted that the rebels had committed crimes against humanity.
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