EU foreign affairs chief Federica Mogherini pressed Libyan politicians to support a unity government Thursday, a day after suicide bombings killed dozens sparking fears of a jihadist expansion on Europe's doorstep.

Mogherini issued a plea for unity as she met in a suburb of Tunis with Fayez al-Sarraj, a businessman who was named in a UN-brokered national unity government as prime minister designate.

"Libyans deserve peace and security," she said.

"With the Libyan Political Agreement, with a presidency council, the government of national accord that we hope can be put in place soon, there is finally after so many months a real possibility to unite among Libyans and try to fight terrorism," she said.

The Libyan branch of ISIS group said it was behind one of Thursday's attacks, on a checkpoint in Ras Lanouf, home to a key oil terminal on the country's northern coast.

IS, which launched an offensive against Libya's oil heartland on Monday, said a foreign fighter detonated an explosives-packed car, killing and wounding several people.

The Red Crescent said six people, including a baby, died in the attack.

Another suicide bomber on Thursday attacked a police training school in Zliten, west of Tripoli, killing more than 50 people, a security source said.

So far, nobody has claimed responsibility for that attack, which left buildings charred and turned cars into twisted wrecks.

It was the deadliest single attack in Libya since the 2011 revolution that toppled longtime dictator Muammar Gaddafi.

Fears the jihadists are establishing a new stronghold on Europe's doorstep have added urgency to efforts to bring together warring factions in a country beset by chaos since 2011.

Libya has had rival administrations since August 2014, when an Islamist-backed militia alliance overran Tripoli, forcing the government to take refuge in the east.

In December, after months of negotiations, a minority of lawmakers from both sides signed on to the UN-brokered national unity deal which has yet to win the full support of the two legislatures.

Analysts say these divisions are bolstering the position of ISIS.

"The situation has become very worrisome... with IS taking advantage of the chaos, the collapse of the central authorities and wars by proxy," said Karim Bitar, head of research at the French Institute of International Relations.

The international community has been pleading for months with Libya's rival parliaments to embrace the UN-brokered deal.

Mogherini was to hold talks later Friday in Tunis with the members from both legislatures who signed the agreement. She will be making a fresh bid to shore up support for the deal.

"As the Libyans express the courage and the willingness to unite, to put the country back on track... Europe, the international community is there to show its own unity in supporting this process," she told reporters after meeting Sarraj and before heading into the talks.

UN Secretary General Ban Ki-moon condemned Thursday's attacks and also urged unity among Libyans.

"These criminal acts serve as a strong reminder of the urgency to implement the Libyan political agreement and form a government of national accord," Ban said.

"Unity is the best way for Libyans to confront terrorism in all its forms."

Bitar said the establishment of a national unity government was a matter of "urgency" but he warned that international efforts could fail due to "numerous suspicions" on the ground.

Mohamed Eljarh, a non-resident fellow with the Atlantic Council's Hariri Centre, agreed.

He said the latest attacks claimed by ISIS "would not end the feud in Libya, but could at best result in reducing the trust deficit between the various armed and political groups as they attempt to cooperate and help each other in the face of IS's expansion".

The heads of Libya's parliaments have warned the UN-brokered deal has no legitimacy and that the politicians signing the agreement represented only themselves.

The chaos that has gripped Libya since the 2011 revolution has also led to its rise as a stepping stone for migrants crossing the Mediterranean to Europe.

The ISIS offensive against the oil terminals in Ras Lanouf and nearby Al-Sidra in Libya's so-called "oil crescent" came as ISIS has tried for weeks to push east from its stronghold in Sirte.

Officials have warned the already crumbling state could be paralysed if ISIS, which is reported to have at least 3,000 fighters in Libya, seize control of oil resources.

In a report to the UN Security Council in November, International Criminal Court chief prosecutor Fatou Bensouda said ISIS was responsible for at least 27 car and suicide bombings in Libya in 2015.