Israel agreed to an Egyptian request and opened its border crossings with the Gaza Strip on Tuesday despite Palestinian mortar fire that violated a three-week-old truce.

The request from Egypt was an attempt to prod forward the cease-fire, which was designed in part to ease Israel's crushing blockade of the coastal strip. In so doing, Israel suggested it might stop automatically closing the crossings in response to every truce violation, like the mortar shell Palestinian militants fired Monday.

Hours after the crossings opened at noon, militants fired another shell into Israel, causing no casualties or damage, the Israeli military said. No Palestinian group immediately claimed responsibility for the fire, and Israel kept the crossings open.

In all, 13 rockets and mortars have been fired from Gaza since the truce began. In response, Israel has kept the crossings closed about half of the time since the truce took effect June 19.

Under the first phase of the cease-fire, Gaza militants were to halt their assaults on southern Israel, and Israel was to gradually allow more supplies to enter impoverished Gaza, home to 1.4 million Palestinians.

For months, the crossings have been cracked open only for humanitarian shipments, in an effort to pressure militants to stop barraging southern Israel with rockets and mortars. The closures had led to widespread shortages of fuel, electricity and basic goods in Gaza.

So far the truce has not eased conditions in Gaza because of the frequent closures.

Should the truce take root, its final stage calls for stepped-up talks on opening a major Gaza border passage with Egypt and releasing an Israeli soldier Hamas has held for two years. Hamas officials were headed to Cairo on Tuesday to discuss opening the Gaza-Egypt passage.

Egypt mediated the truce because Israel has no contacts with Hamas, which does not recognize the Jewish state's right to exist.

In related news, an explosion went off early Tuesday at a Hamas military training camp in Gaza, killing two members of the Islamic militant group and wounding three, both health and Hamas officials said.

Hamas' military wing said in a statement that the two were killed while carrying out a "holy mission," suggesting explosives were mishandled and went off prematurely.

The Israeli military said it was not involved.

While trying to cement a truce with militants in Gaza, Israel is also cracking down on Hamas operations in the West Bank.

For a second straight day Tuesday, the Israeli military ordered the shutdown of facilities it said were affiliated with Hamas in the West Bank town of Nablus. Palestinians said the military seized a five-story mall and ordered the building's 70 shop owners to vacate the premises by mid-August.

"I don't know where to go now," said Omar al-Khayyat, who has owned a cafeteria and coffee shop at the mall for five years.

Israeli defense officials said the mall's owners were linked to Hamas and that the raid was part of an effort to cripple the group's economic infrastructure in the West Bank. The officials said spoke on condition of anonymity because they were not authorized to discuss details with the media.

Hamas violently wrested control of the Gaza Strip a year ago, and Israel doesn't want it to take over the West Bank, too. In recent months it has gone after West Bank charities, moneychangers, media and schools with suspected ties to militants.

Elsewhere in the West Bank, the Israeli military lifted a two-day curfew that confined residents of a Palestinian village to their homes and barred movement in and out of the community.

The army imposed the curfew on Naalin on Sunday after violent protests against Israel's West Bank separation barrier. The barrier, designed to keep Palestinian attackers out of Israel, dips into the West Bank at points and is designed to cut through village land.

Officials at local hospitals said two people were hospitalized during the unrest. One man was shot in the leg and another in the stomach, hospital officials said.

Maj. Avital Leibovich, an army spokeswoman, said soldiers opened fire overnight when dozens of people staged a "violent riot" against the barrier, throwing rocks at soldiers. She said the soldiers attempted to disperse the crowd, then opened fire at three protest leaders, hitting them in the legs.

The curfew was lifted after army commanders met with local village leaders, who promised future protests would be peaceful, an army statement said. Palestinians denied they had reached an agreement with the military.