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Three top Islamist militants were killed in two separate operations by Egyptian police, the government said on Tuesday.

The two militants killed in New Cairo were senior members of the Hasm group - a movement the government accuses of links to the outlawed Muslim Brotherhood, the interior ministry said.

The third man, a militant who was gunned down in the restive North Sinai province, was a leader of a militia affiliated with the Islamic State group, the ministry said in a separate statement.

Two others were caught trying to move to a new hideout on Cairo's outskirts.

In the first operation, authorities had acted after learning that some of Hasm's leaders were about to move "equipment and weapons" to a new hideout in New Cairo, outside the capital's ring road, the ministry said.

Security forces set up checkpoints on roads to the area and as forces approached a suspect car, "its passengers opened fire" on police and were killed in retaliatory fire.

The two were identified as students aged 24 and 21 who were "among the most prominent leaders in the Hasm terrorist group," the ministry said.

In the vehicle, police found seven automatic weapons, two other firearms, a large amount of ammunition, masks and radio equipment.

The ministry did not say when the shootout took place, but said the group had been planning to move locations on Tuesday.

The militants who died were said to have been behind attacks including a shootout in early May in which three policemen were killed and five wounded near the Cairo ring road.

The pair had carried out attacks on the orders of "their leaders who have fled abroad," the ministry said.

Last month, Hasm claimed responsibility for an attack that killed two police officers and injured three conscripts in Cairo.

The unidentified assailants planted an explosive device in the upscale Cairo suburb of Maadi, detonating it remotely when the police vehicle drove by, the group said at the time.

It vowed more attacks in the coming months.

Egypt has been facing a deadly Islamist insurgency that has killed hundreds of policemen and soldiers since the army overthrew President Mohamed Morsi in 2013 and crackdown on his supporters.

In February, an Egyptian court declared Hasm a terrorist organisation, alleging it was linked to the outlawed Muslim Brotherhood group.

Little is known about the movement but analysts distinguish them with militant organisations such as the Islamic State group which has a presence in the Sinai.