* Israeli towns near Gaza on alert
* Palestinians pick through rubble at bombing sites
* Netanyahu cuts U.S. visit short to return home
* Palestinians say Egypt mediated truce (Adds scene in Gaza, southern Israel)
By Nidal al-Mughrabi and Ari Rabinovitch
GAZA/JERUSALEM, March 26 (Reuters) - Cross-border fighting between Israel and Hamas abated on Tuesday after a day of Palestinian rocket attacks and Israeli air strikes, but tensions remained high with Israeli forces massed along the Gaza frontier.
Rocket warning sirens continued to sound in Israeli towns near the border late on Monday after Palestinian officials said Egypt had mediated a truce. But by Tuesday morning, the border area had fallen quiet.
The flare-up began early on Monday when seven Israelis were wounded near Tel Aviv by a rocket fired from the Gaza Strip, some 120 km (70 miles) away.
Hours later Israel - which blamed Hamas, the dominant armed force in Gaza, for the rocket attack - carried out a wave of retaliatory strikes, wounding five Palestinians. The military said extra soldiers and tanks had been moved to the border.
Gaza militants fired barrages of rockets into Israel late into Monday night. Some were shot down by Israeli defenses and others landed in empty areas.
The escalation came just two weeks before an election in which Prime Minister Benjamin Netanyahu is fighting for his political life after a decade in power, campaigning on a tough line against Palestinian militants.
Beset by corruption scandals, he faces a strong challenge from a centrist coalition led by a top general.
Netanyahu cut short a visit to the United States, after meeting President Donald Trump, and was due to land in Tel Aviv later in the day.
Boarding his flight back home, Netanyahu said Israel had delivered "a very, very forceful response".
"WE DON'T WANT WAR"
Israel remained on high alert on Tuesday and the military said it remained "prepared for various scenarios".
Israeli schools near the border were closed and residents instructed to stay near bomb shelters.
"I told my kids that everything is going to be all right and that it will be over. We trust the government will solve the problem," Eliav Vanunu, whose house in the Israeli border town of Sderot was damaged by a rocket on Monday night, said on Israel Radio.
In Gaza, some universities were shut but public schools were open, although many families kept their children home.
Palestinians picked through the rubble of destroyed buildings to search for valuables and documents.
The office of Hamas chief Ismail Haniyeh was one of the initial targets hit on Monday, although he was likely to have been evacuated in advance.
"We don't want war, but if Israel wants it then what should we do? We ask our factions to respond," said Mohammad Sayed, 40. "But we hope Egypt reaches a deal to end this."
Israel has waged three wars on Gaza since Hamas took control of the territory in 2007. Israeli air strikes in retaliation for rockets from Gaza are a frequent occurrence, but Israel's swift mobilisation of extra troops to the border area was unusual. (Reporting by Nidal al-Mughrabi, Ran Tzabari and Ari Rabinovitch; Writing by Jeffrey Heller; Editing by Andrew Heavens)
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