Pentagon officials say the US and the UK have fired more than 110 missiles, while French planes struck pro-Gaddafi forces attacking rebel-held Benghazi.
Col Gaddafi has vowed retaliation and said he would open arms depots to the people to defend Libya.
Cruise missiles hit air-defence sites in the capital, Tripoli, and Misrata.
Libyan state TV said 48 people had been killed and 150 wounded in the attacks. There was no independent confirmation of the deaths.
A French plane fired the first shots against Libyan government targets at 1645 GMT on Saturday, destroying a number of military vehicles, according to a military spokesman.
UK Prime Minister David Cameron confirmed that British planes are in action over Libya.
Despite the fact that it was French war planes which launched the first attacks, it is clear that this early phase of the operations is an overwhelmingly American affair – all but a very small number of cruise missiles have been fired from American ships and submarines.
Only they have the capability to inflict the sort of damage to Libya’s air defences that is needed before a no-fly zone can be safely patrolled, a point alluded to by President Barack Obama even as he repeated the limits of American involvement.
President Obama has launched these attacks with great reluctance and seems anxious that this not be interpreted as yet another American-led foray into the Arab world.
But for all his desire to be seen to take a back seat, he and everyone else knows that this sort of thing does not happen unless Washington is deeply involved.
US President Barack Obama, speaking during a visit to Brazil, said the US was taking “limited military action” as part of a “broad coalition”.
“We cannot stand idly by when a tyrant tells his people there will be no mercy,” he said.
He repeated that no US ground troops would take part.
After the missile bombardment and the air strikes, Col Gaddafi made a brief speech calling on people to resist.
“Civilian and military targets in the air and sea will be liable to serious danger in the Mediterranean,” he said.
“Arms depots are now open and the masses are being equipped with all sorts of weapons in defence of Libya’s independence, unity and honour,” the Libyan leader warned.
He called the attacks “a colonialist crusade of aggression. This can lead to open a new crusade war.”
The BBC’s Kevin Connolly, in the rebel-held eastern city of Tobruk, says it is now clear that Col Gaddafi’s strategy is to portray the attacks as an act of colonialist aggression and rally enough of the Libyan people behind him to maintain his grip on power.
The UK Ministry of Defence said a British submarine and a number of Tornado jets had fired missiles at Libyan military targets.
Mr Cameron said that launching military action against Libya was “necessary, legal and right”.
Libyan state TV reported that what it called the “crusader enemy” had bombed civilian areas of Tripoli, as well as fuel storage tanks supplying the western city of Misrata.
Sources in Tripoli told BBC Arabic that the attacks on the city had so far targeted the eastern areas of Sawani, Airport Road, and Ghasheer. These are all areas believed to host military bases.
Shortly after 0200 Libyan time (0000 GMT) on Sunday morning, heavy bursts of anti-aircraft fire arced into the sky above Tripoli and several explosions were heard.
• US: Firing guided missiles from USS Barry and USS Stout; providing amphibious warships, and command-and-control ship USS Mount Whitney
• France: Carried out mission with at least 12 warplanes including Mirage fighters and Rafale jets; deploying aircraft carrier, warships
• UK: Providing Typhoon and Tornado jet fighters; surveillance planes; HMS Westminster and HMS Cumberland; submarines
• Italy: Nato base at Naples understood to be central hub; other Mediterranean bases made available
• Canada: Providing six F-18 fighter jets and 140 personnel
• UN’s calculated gamble
• Libya no-fly zone: Aircraft
The strikes on Misrata targeted a military airbase, the Reuters news agency reported, quoting two residents who denied the state TV reports that fuel stores were hit.
The cruise missiles were fired from one British submarine and a number of American destroyers and subs, said a Pentagon official.
The missiles hit more than 20 air-defence sites along the Mediterranean coast, said Navy Vice Adm William E Gortney.
The action came hours after Western and Arab leaders met in Paris to agree how to enforce the UN resolution, which allows “all necessary measures” to protect civilians from forces loyal to Col Gaddafi.
Our correspondent in Tobruk says that once the air-defence systems are taken out, combat aircraft can patrol and it will then become clear if they will attack Col Gaddafi’s ground forces. It is this that will determine the outcome of the
Earlier on Saturday, pro-Gaddafi forces attacked Benghazi despite declaring a ceasefire a day earlier.
Reports from the city said that government tanks and artillery had bombarded the city and there was fighting around the university.
Rebels in the city said thousands of people were fleeing the attack, heading east, and the UN refugee agency said it was preparing to receive 200,000 refugees from Libya.
Journalists later said the bombardment ended in the late afternoon and that rebel forces remained in control of Benghazi.
The Libyan government blamed the rebels for breaking the ceasefire and said its forces had fought back in self defence.
French planes are reported to have hit government tanks and armoured vehicles around Benghazi.
French planes also flew reconnaissance missions over “all Libyan territory”, military sources in Paris said earlier.
In addition, Canada is sending warplanes to the region, while Italy has offered the use of its military bases. A naval blockade against Libya is also being put in place.
The international community was intervening to stop the “murderous madness” of Col Gaddafi, French President Nicolas Sarkozy said.
“In Libya, the civilian population, which is demanding nothing more than the right to choose their own destiny, is in mortal danger,” he warned. “It is our duty to respond to their anguished appeal.”
Shortly after the airstrikes began, Libyan state TV said a French plane had been shot down near Tripoli. However, French military officials said all their planes had returned safely.
Col Gaddafi has ruled Libya for more than 40 years. An uprising against him began last month after the long-time leaders of neighbouring Tunisia and Egypt were toppled.
-Paul Adam, BBC