Hamas militants fired a rocket into an Israeli border village, wounding two young sisters as they played outside their home. The attack followed Israel air strikes against Gaza militants and threats of an "all-front" war on the Islamic group.

The rapid-fire events threatened to escalate into large scale combat that could bury U.S.-led Mideast peace efforts.

Hamas stepped up its rocket barrages at southern Israel for a second day, retaliating for an Israeli strike that killed seven of its police officers. More than a dozen rockets rained down, one exploding at Kibbutz Beeri, a communal village about four miles from the border fence.

Two sisters, ages 12 and 2, were lightly wounded as they played in their yard, police said. Their mother was taken to a hospital for shock.

Israel unleashed an intensified air campaign after Hamas claimed responsibility for a suicide bombing Monday that killed one woman in southern Israel. It was the first such Hamas attack in Israel in more than three years.

Early Wednesday, Israeli aircraft fired at militants who launched rockets moments earlier, the military said. Hamas said that four of its men were wounded. After nightfall Wednesday, Israeli aircraft hit a metal workshop in Gaza city, Hamas said. No one was hurt. The military had no immediate comment.

The upsurge in fighting threatened to overwhelm peacemaking efforts in an avalanche of rocket attacks, reprisals and bombings.

A poll released Wednesday showed Hamas jumping in popularity for breaking down a border wall with Egypt on Jan. 23, allowing Gaza's quarantined people a 12-day taste of freedom before Egypt closed the breaches Sunday.

Israel on Wednesday approved construction of a fence along the 150-mile desert border with Egypt, fearing that Palestinian militants who crossed from Gaza into Egypt could infiltrate into Israel.

The issue of the border has arisen several times since the border was established in 1982. Most recently, Israel pledged to build a border fence in early 2007, after a suicide bomber infiltrated from Egypt and killed three Israelis in the southern port of Eilat. It considered the issue again after an upsurge in smuggling and an influx of African refugees.

Despite Wednesday's decision, no funds were budgeted, and it was not clear when construction would start.

At first, Israel assumed the bomber who hit the southern town of Dimona on Monday came in from Egypt, but Hamas identified the bombers as militants from the southern West Bank city of Hebron.

Hamas official Sami Abu Zuhri defended the suicide bombing.

"There is no choice, no option for our people, but to resist the occupation and defend themselves by all possible means," he told The Associated Press.

With the suicide bombing and its renewed involvement in rocket attacks, Hamas was showing it could be an effective spoiler in peace efforts.

Hamas does not recognize Israel and has sent dozens of suicide bombers to attack inside the country. The Islamic militants, who rule Gaza after expelling forces loyal to moderate Palestinian President Mahmoud Abbas last June, are not a party to peace talks renewed at a U.S.-sponsored conference in November.

Israel insists that Abbas must retake control of Gaza and neutralize militants before any peace accords are implemented. For the meantime, the balance of power is tilting toward Hamas.

While Hamas gains clout among Palestinians by breaking Israel's stranglehold on Gaza, even temporarily, Abbas' administration is coping with a strike by civil servants protesting a new regulation aimed at forcing West Bank residents to pay millions of dollars in back utility bills.

The strike showed that despite the renewal of foreign aid to Abbas' regime, Palestinians under his control are still in serious economic trouble.

So are Palestinians in Gaza, but many are united in blaming Israel for their troubles. Israel, for its part, planned to keep up its economic pressure on Gaza. Last week Israel's Supreme Court cleared the way for reduction in electricity supplies starting Thursday.

Israel indicated that it would not let up in its attacks.

"We need to understand there is a war in the south," Vice Premier Haim Ramon told Israel Radio. "The war against Hamas has to be fought on all fronts."

In Gaza, the Hamas-dominated legislature canceled Wednesday's session, fearing an Israeli attack. The Israeli military refused to comment.

It was unlikely that Abbas could press ahead with serious peace talks during a high-profile conflict between Israel and Hamas. Abbas has been forced to periodically condemn Israeli attacks in the name of Palestinian solidarity.

On Wednesday, Abbas condemned the rocket fire but urged Israel to let supplies in.

"These rockets that are being fired at Israel must stop. It's pointless," he said at a news conference with Austria's foreign minister. "At the same time, Israel should not use these rockets as a pretext for collective punishment on Palestinians in Gaza."