The sources said the woman, who carried no identity papers but was believed to be an Eritrean in her 30s, was shot dead and a man was wounded after police fired on a group of at least 10 Eritrean migrants overnight. Five children were among the group.

"The Egyptian police were obliged to open fire on a group of Africans after they refused to stop and tried to flee in the direction of Israeli territory," one security source said, speaking on customary condition of anonymity.

The death brings to six the number of African migrants who have been killed trying to cross the Egypt-Israel border since the start of the year.

Rights group Amnesty International says Israel has put pressure on Egypt to reduce the flow of people crossing the border illegally, and Amnesty has called for an investigation into the killings.

In two separate incidents hours after the Eritrean woman was killed, police shot and wounded an 18-year-old migrant from Ivory Coast and a 28-year-old migrant from Sudan.

Police arrested 13 migrants from all three incidents, including the five Eritrean children and the three adults who were wounded, the sources said.

Amnesty says thousands of migrants try to cross into the Jewish state from Egypt each year, with numbers rising since 2007. Egypt's Sinai peninsula is the main route for traffickers trying to take mainly African migrants, including many from Sudan and a growing number from Eritrea, into Israel.

The migrants are seeking work or asylum away from conflict at home and harsh living conditions in Egypt, where activists say African migrants face economic marginalisation and racism.