Egypt's president has called for a UN-backed coalition to rid Libya of Islamic militants.
Abdel-Fattah el-Sissi, speaking to France's Europe 1 Radio, said Egyptian air strikes against Islamic State (IS) positions in Libya were in self-defence.
Mr el-Sissi, a general-turned-politician, said: "We will not allow them to cut off the heads of our children."
Asked whether he wanted to see a UN-backed coalition for Libya, he said: "I think there is no choice."
Egypt's air strikes on Monday were in retaliation for the mass beheading on a beach of Egyptian Coptic Christians. A video of the killings was released by IS late on Sunday.
Mr el-Sissi said: "We have abandoned the Libyan people as prisoners of the militias. The militias have to give up their arms and must work in a civil context. We have to disarm and prevent arms from falling into the hands of extremists.
"What happened is a crime, a monstrous terrorist crime that our children have their throats cuts in Libya and not to react. It's a kind of self-defence accepted by the international community."
The Egyptian attacks drew harsh criticism from Omar al-Hassi, the militia-supported prime minister in Tripoli. Libya's elected and Western-backed parliament and government were forced to convene outside Tripoli when the capital was overrun by Islamic and tribal militias last year. An older parliament, supported by the militias, declared itself legitimate and formed a rival government with Mr al-Hassi at the head.
"This treacherous aggression and the terrorism carried out by the Egyptian air force is a violation of Libyan sovereignty and a scandalous violation of the UN charter and international law," said Mr al-Hassi, who accused the Egyptians of attacking Libya "without any solid proof" that they were striking the militants responsible for killing the Egyptian Christians.
Mr el-Sissi has spoken with France's president and Italy's prime minister about Libya and sent his foreign minister Sameh Shukri to New York to consult at the UN ahead of a terrorism conference opening tomorrow in Washington.
France, a lead player in the campaign to oust Libya's dictator Muammar Gaddafi in 2011, has campaigned for months for some kind of international action in Libya and announced a deal on Monday to sell 24 advanced fighter jets to Egypt. French troops are already in place near Libya's southern border in Niger as part of a counter-terrorism force.
French president Francois Hollande's office said he and Mr el-Sissi "stressed the importance of the Security Council meetings and that the international community takes new measures to confront this danger".
A Nato official said: "There is no discussion within Nato on taking military action in Libya," but added that Nato is ready "to support Libya with advice on defence and security institution-building".
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