Egyptian police shot dead an Eritrean woman as she tried to cross the border illegally into Israel when she ignored warnings to stop, a security source said on Monday.

"The woman in her thirties was shot in the chest after she ignored police orders to stop. She died instantly," the source told AFP.

"An Eritrean man, 30, was also shot in the foot as he tried to escape and is now being treated in hospital," the source said.

The two were part of a group of 10 Africans trying to cross into Israel late on Sunday when they were spotted by a routine border patrol.

In another incident, a Sudanese national and an Ivorian were each shot in the leg as they tried to cross into Israel from the Karm Abu Salem (Kerem Shalom) crossing, the source added.

On Tuesday, a 50-year-old Sudanese man was shot dead while trying to cross into Israel south of the town of Rafah.

The 250-kilometre (155-mile) Egyptian-Israeli border has become a major transit route for migrants and asylum-seekers.

Dozens of migrants, mainly Africans, have been arrested in recent months as Egyptian police try to halt the constant stream into Israel. Several have been killed while trying to make the crossing.

The UN refugee agency said earlier this month that more than 1,500 Africans, mostly from Eritrea, have entered Israel illegally through Egypt since the start of the year.

On Sunday Israeli Prime Minister Ehud Olmert ordered security authorities to deport to Egypt migrants who entered the country illegally and to tighten surveillance of the Israel-Egypt border.

An official in Israel's public security ministry has said that more than 4,700 people entered Israel from the Sinai over the past 14 months alone.