More than 30 people have been killed today in a series of car bomb explosions in the eastern Libyan city of Qubbah.
Parliamentary speaker Aguila Saleh told Al-Arabiya TV that a petrol station and a security building had been the targets of the bombs.
The State of Qatar has reportedly recalled its ambassador based in Cairo amid disputes over Egypt's decision to carry out air strikes in Libya.
According to state news agency QNA, the director of Arab affairs at the Qatari foreign ministry voiced concern at an Arab League meeting in Cairo over the decision to carry out air raids in Libya without consultation with other Arab states.
Egypt has carried out a number of air strikes after militants claiming to be alligned to Islamic State extremists beheaded 21 Egyptian Christians.
Libya has asked the United Nations Security Council to lift an arms ban so its army can equip itself to fight Islamic State militants.
The country's Foreign Minister Mohamed Dayri said: "Libya needs a decisive stance from the international community to help us build or national army's capacity.
"This would come through a lifting of the embargo on weapons so our army can receive material and weapons so as to deal with this rampant terrorism."
Currently the Libyan government is allowed to import weapons and related materiel but only with UN approva following the ban imposed in 2011.
David Cameron stressed Britain "has not abandoned Libya" after Egypt bombed Islamic State targets in the country in response to the murder of 21 Egyptian Christians.
"What we face in Libya is a very difficult situation, with far too many armed militias, without a proper government and with the growth of ungoverned space," the Prime Minister said.
"What the whole world needs to do is come together and work for Libya that has a national unity government."
Egyptian President Abdel Fattah Al-Sisi called for a United Nations resolution mandating an international coalition to intervene in Libya after its jets bombed Islamic State targets there.
"There is no other choice, taking into account the agreement of the Libyan people and government and that they call on us to act," he told France's Europe 1 radio.
Asked if Egypt would resume its own action, he said: "We need to do it again, and all of us together."
Egypt has opened a new front in the war against so-called Islamic State, bombing targets on the doorstep of Europe. It launched two waves of airstrikes on the Islamist terrorists in Libya.
It follows the mass murder of 21 Egyptian Christians on the Libyan seafront, barely 200 miles from the frontier of Europe. The Egyptian government has called on the international community to intervene in Libya.
ITV News Africa correspondent John Ray reports:
The bombing of Libya was a unilateral Egyptian air-force strike. Relations between the el-Sissi regime and Washington are poor, and yes Washington would have watched this strike unfold in real time.
I think there is a bigger strategic point here as well. How does the West tackle these sorts of crises in North Africa and the Middle East. We have tried intervening in Libya and it has led to almost total chaos. We've tried not intervening in Syria and we are left with a humanitarian catastrophe.
So it really means that there is no template, no model for success, and we are left with what we are seeing now. A deteriorating situation right across the region.
David Cameron has spoken to Egyptian president Abdel Fattah el-Sisi to offer his condolences over the murder of the Egyptian Christians and to discuss how Britain and Egypt could work together to fight terrorism.
Mr el-Sisi and the Prime Minister agreed that a political solution was the best way to solve the Libyan crisis.
"The Prime Minister recognised that Egypt, as one of Libya's neighbours, had a particular interest in protecting itself from violent extremism on its borders and that both countries shared the same objective: a safe and secure Libya," a Downing Street spokeswoman said.
Egypt has called on the US-led coalition fighting Islamic State in Iraq and Syria to broaden the scope of their operations to include Libya, highlighting how the insurgent group has expanded its reach around the Arab world.
After the strikes, Egyptian president Abdel-Fattah el-Sissi spoke with France's president and Italy's prime minister about the Libya situation.
"What is happening in Libya is a threat to international peace and security," said el-Sissi, who also banned all travel to Libya by Egyptian citizens.
Libya's air force also participated in the air strikes on Libya, which targeted Derna, an eastern coastal city regarded as a base for fighters of the so-called Islamic State.
"There are losses among individuals, ammunition and the (Islamic State) communication centres," Libyan air force commander Saqer al-Joroushi told Egyptian state television, adding that dozens had been killed.
Joroushi, who is loyal to Libya's internationally recognised government, which set up camp in the city of Tobruk after losing control of the capital Tripoli, said there would be more strikes on Tuesday.