A woman, 26, was caught in the crossfire and injured in the leg.
The Israel Defense Forces (IDF) said about 15,000 Palestinians gathered along fence.
Israeli police said on Saturday they were investigating the death of a Palestinian woman in the occupied West Bank, after her husband said he suspected Israeli settlers had pelted their vehicle with rocks. The search is still on for the gunman, whose sister was arrested Thursday in connection with the attack.
Tamer Abu Ermanah, 27, was shot and killed by Israeli soldiers east of the town of Rafah, in the southern Gaza Strip, he said.
The Palestinian Ministry of Health announced the killing of Aisha al-Rabi (48 years) from Badia village from Salfit governorate north of west bank following an attack by Israeli settlers threw stones at her husband auto.
Palestinian mourners across the Gaza Strip have held funerals for seven protesters killed a day earlier.
The Israeli army said five were shot dead after breaking through the border fence and attacking an army post.
She died in hospital in the northern West Bank city of Nablus from a head injury sustained in the stone-throwing incident south of the city on Friday, Wafa said, citing medical and Palestinian security sources.
"Israel will not tolerate a situation in which fuel tankers are allowed to enter Gaza on the one hand, while terror and violence are used against [Israeli] soldiers and Israeli citizens on the other", said Defence Minister Avigdor Lieberman.
Israeli fire has killed 155 Palestinians during the protests since they began in March.
A wave of mainly lone-wolf Palestinian attacks against Israelis in the West Bank erupted in 2015 but had largely abated.
Israeli soldiers on Friday opened fire at Palestinian protesters, killing five and wounding 50, according to Palestinian health officials. No Israeli troops were harmed, the army added.
Since March, Hamas has orchestrated near-weekly protests along the fence.
Israeli army spokesman Jonathan Conricus said around 20 Palestinians had crossed the border in an "organised attack" after an explosive device destroyed a portion of the fence.