BEIT LAHIYA, Gaza, (Reuters) – Israeli forces on the offensive in Gaza killed 12 Palestinians in air strikes and clashes with militants on Thursday in the worst violence since the Jewish state quit the strip a year ago.

Gunmen also killed an Israeli soldier in northern Gaza, where clashes raged, Al Jazeera television said.

Prime Minister Ehud Olmert ordered tanks to push deeper into Gaza overnight after militants from the ruling Hamas movement fired rockets into a major Israeli city for the first time.

The incursion expands an offensive that began last week with the main goal of bringing home a captured soldier and piles pressure on the Hamas government, already on the brink of collapse because of a Western aid embargo.

Among the deadliest attacks on Thursday, an Israeli air strike near the town of Beit Lahiya in northern Gaza killed six Palestinian civilians, witnesses and medics said.

The army said it had carried out two air strikes against armed militants in the area, killing four gunmen. A spokeswoman said she was unaware of civilian deaths.

Beit Lahiya was also scene of the heaviest ground fighting, where gunmen from various factions fired anti-tank rockets in running battles with Israeli troops who were backed up by tanks and helicopter gunships.

The army said three soldiers were hurt, one seriously.

Beit Lahiya’s streets were largely deserted as frightened residents sheltered indoors.

“Israeli tanks are outside our house. Children are screaming and the house is shaking. We are caught in the crossfire,” one woman told a local radio station.

Aircraft also launched missile strikes near the southern town of Khan Younis.

The Palestinian death toll is the highest in a single day since Israeli forces killed 16 people in October 2004 in a raid on a Khan Younis refugee camp.

The flare-up in violence has dashed any lingering hopes peace talks might be revived.

Defence Minister Amir Peretz said that although Israel quit Gaza last year after 38 years of occupation, “no one should see that as a guarantee that we cannot reach territory in which we feel we have no choice but to operate”.

“We have no intention of sinking into the Gaza swamp.”

Tanks earlier pushed into the ruins of three of the 21 Jewish settlements evacuated when Israel left Gaza last year.

The military said Israeli forces would stay in the area, several kilometres inside northern Gaza, “until the completion of their mission”. Rockets are often fired from the former northern Gaza settlements at Israel.

Olmert’s office has said the offensive will not amount to re-occupying parts of the strip long-term.

Officials from the Hamas-led government have made little comment on the incursion but Palestinian residents voiced fears the Israeli forces were there to stay.

Hamas rockets hit Ashkelon, a city of 115,000, on Tuesday and Wednesday. It was the furthest point hit by the missiles, which cause few casualties but spread panic.

The stepped-up incursion has put the heat on the Palestinian government, already facing Israeli threats over the abduction of Corporal Gilad Shalit on June 25. Hamas gunmen were among those who seized him.

Palestinian government spokesman Ghazi Hamad said the embattled administration was interested in solving the crisis caused by Shalit’s capture.

“We don’t want Gaza destroyed nor do we want attacks. And you want him to return to his family,” Hamad told Israel Radio without elaborating.

Israel has dismissed demands of a prisoner swap for his release.

Twenty two Palestinians, the majority of them militants, have been killed since the offensive began. Israel has also detained dozens of Hamas officials.