At least five Palestinian was killed and dozens were injured in Qalandia, near the West Bank city of Ramallah.
The violence came after a United Nations school in Gaza that was crowded with hundreds of Palestinians seeking refuge from fierce fighting came under fire. At least 15 civilians were killed.
UN Secretary-General Ban Ki-moon angrily denounced the school attack, saying the killing must "stop now".
But the frantic diplomatic efforts spanning the region were running into a brick wall. Israel demands Hamas stop firing rockets without conditions, while Gaza's Islamic militant rulers insist the seven-year Israeli-Egyptian blockade of the territory must end first.
The UN said it had been trying to achieve a humanitarian pause in the fighting to allow the evacuation of civilians from the area.
Fighting has been fierce across Gaza and at least 119 Palestinians were killed yesterday, making it the bloodiest day of the 17-day war.
That raised the overall Palestinian death toll to at least 803, Gaza health official Ashraf al-Kidra said.
Israel has lost 32 soldiers, all since July 17, when it widened its air campaign into a full-scale ground war. Two Israeli civilians and a Thai worker in Israel have also been killed by rocket or mortar fire.
Israel says the war is meant to halt the relentless rocket fire on its cities by Palestinian militants in Gaza and to destroy a sophisticated network of cross-border tunnels that Hamas is using to sneak into Israel to try to carry out attacks inside communities near the border.
Israel insists it does its utmost to prevent civilian casualties but says Hamas puts Palestinians in danger by hiding arms and fighters in civilian areas.
The attack on the UN school in Beit Hanoun was likely to increase pressure on international diplomats shuttling around the region in an effort to broker a cease-fire.
More than 2,300 rockets have been fired at Israel from Gaza since July 8, and the Israeli military says it has uncovered 31 tunnels leading from Gaza to Israel, some of which have been used by Hamas to try to carry out attacks inside Israel.
Israeli aircraft struck 30 houses in the Gaza Strip yesterday, killing a leader of the militant Islamic Jihad group and two of his sons.
Ground troops and Hamas gunmen fought intense battles in the north and centre of the territory.
The Israeli military said it hit 45 sites in Gaza, including what it said was a Hamas military command post, while Gaza militants continued to fire dozens of rockets at Israel, with one hitting an empty house.
Hamas has said it will not halt fire without international guarantees that Egypt and Israel will open Gaza's border crossings and end their seven-year-old blockade. Israel and Egypt are reluctant to ease the blockade, fearing this will enable Hamas to tighten its grip on Gaza.
Israeli government spokesman Mark Regev said Hamas chief Khaled Mashaal has "put so many preconditions on a ceasefire so as to make it impossible".
Over the past two weeks, Israeli aircraft have repeatedly hit homes of Hamas and Islamic Jihad leaders.