Five gunmen who killed 16 Egyptian guards near the border with Israel before crossing into the Jewish state in an armored vehicle have been killed, an Israeli army spokesperson said Monday.

"The bodies of the five gunmen have been found by the Israeli army," the spokesperson said a day after the incident, but did not give details.

An Egyptian medical official said earlier that gunmen in Bedouin attire drove up in two vehicles to the checkpoint near the Karm Abu Salem border crossing and opened fire.

The Health Ministry said 16 soldiers and border guards were killed, while a security official said another seven were wounded.

Egypt's state-run MENA news agency said the gunmen were "jihadists" from inside the Hamas-run Gaza Strip.

Speaking after an emergency meeting with military officials, the interior minister and the intelligence chief, Egyptian President Mohamed Morsy vowed to retake control of the Sinai after the attack.

"The [security] forces will take full control of these regions," Morsy said in a TV address.

He had given "clear instructions" that Egypt must take "full control of the Sinai," after the security situation deteriorated markedly following the ouster of longtime strongman Hosni Mubarak early last year.

Morsy, who took the oath of office on 30 June to become the country's first freely elected leader and its first head of state since Mubarak's overthrow, said those who committed the "cowardly" attack and those who worked with them would pay dearly.

"Those responsible for this crime will be hunted down and arrested," he said.