Witnesses in Bengazi, in the east of the country, reported hearing large explosions in the area early on Saturday.
Al Jazeera's Tony Birtley, reporting from Benghazi, told of multiple explosions taking place and a fighter jet being shot down.
Fresh fighting was also reported in the rebel-held towns of Misurata, near the capital Tripoli, and Ajdabiya, which lies close to Benghazi.
The Libyan government denied the reports. "There are no attacks whatesover on Benghazi. As we said, we
are observing the ceasefire," spokesperson Mussa Ibrahim told the Reuters news agency.
Barack Obama, the US president, delivered an ultimatum on Friday to Muammar Gaddafi, threatening military action if the Libyan leader ignored non-negotiable UN demands for a ceasefire.
The warning came shortly after the UN Security Council authorised a no-fly zone over the north African country.
The US also accused the Libyan government of violating the truce.
Within hours of Obama's ultimatum, Susan Rice, the US ambassador to the UN, asked by CNN whether Gaddafi was in violation of these terms, said: "Yes, he is."
The Libyan government, for its part, accused rebel forces in Benghazi of violating the truce.
Khaled Kaim, the Libyan deputy foreign minister, said government forces were "not taking any action against [rebel forces] because we don't want to violate the ceasefire".
Libya's government announced on Friday an immediate ceasefire against pro-democracy protesters.
But residents in Misurata said they faced heavy bombardment through the night on Friday - a charge the Libyan government denied.
Military action 'imminent'
Following the no-fly-zone vote at the UN, a French diplomat said Western military intervention in Libya was imminent.
France is due to host a "decisive" summit on Saturday with the European Union, Arab League and African Union, as well as UN chief Ban Ki-moon, on taking UN-sanctioned military action in Libya.
Gerard Araud, the French ambassador to the UN, said he expected military intervention within hours of the summit.
"The US, the UK and France, we have also launched the ultimatum about the ceasefire ... we have set the conditions," he told BBC.
"So I guess that after the summit, I think that in the coming hours, I think we will go to launch the military intervention."
Obama made clear any military action would aim to change conditions across Libya - rather than just in the rebel-held east - by calling on Gaddafi''s forces to pull back from the western cities of Az Zawiyah and Misurata as well as from the east.
"All attacks against civilians must stop," Obama said on Saturday, a day after the UN Security Council passed a resolution authorising international military intervention.
Braced for battle
"Gaddafi must stop his troops from advancing on Benghazi, pull them back from Ajdabiya, Misurata and Az Zawiyah, and establish water, electricity and gas supplies to all areas. Humanitarian assistance must be allowed to reach the people of Libya," Obama said.
"Let me be clear, these terms are not negotiable... If Gaddafi does not comply ... the resolution will be enforced through military action."
The reports of government forces entering Benghazi's western outskirts on Saturday followed a night of rumours that Gaddafi's troops were within striking distance of the city.
Hundreds of men, some riding in pick-up trucks mounted with machine guns, had flooded out of the city in response to a call from Benghazi's rebel-run radio to swiftly man their posts.
Several loud explosions, some of them followed by anti-aircraft fire, were heard inside Benghazi and new checkpoints sprang up as word spread that Gaddafi's forces could be on their way.
Kaim, Gaddafi's deputy foreign minister, had denied there were any plans to attack the rebel bastion.
Heavy bombardment
At a news conference, Kaim acknowledged that checkpoints had been set up outside rebel-held cities, but stressed that "any sovereign country is free to take [security] measures".
In Misurata, residents said they had faced heavy bombardment on Friday.
Misurata, like Az Zawiyah, had been left stranded in the west while rebels who had advanced towards them from the east were beaten back by a counter-offensive by Gaddafi forces.
A doctor, who declined to give his name, said by telephone late on Friday evening, "now they are on the outskirts of the city [Misurata]. I can still hear bombing from time to time".
In Tripoli the government said there had been no bombing since it announced the ceasefire.
"We have had no bombardment of any kind since the ceasefire was declared," Kaim said, when asked about reports of continued government operations in Misurata and other parts of the country.
