Israeli warplanes targeted more Hamas compounds inside the Gaza Strip on Sunday, in the second day of a military offensive that has killed nearly 300 people.

But militants in Gaza continued to fire increasingly-powerful rockets, which penetrated deeper than ever into southern Israel.

Israeli bombs and missiles also slammed into a police compound, struck a television station and pounded smuggling tunnels on the border with Egypt, which have acted as vital supply lines to the Gaza Strip since the area was blockaded in June 2007.

In what has become the Jewish state's most destructive-ever offensive against Hamas, Israeli officials also indicated the campaign could continue indefinitely.

About 6,500 army reservists have been called up for duty, while infantry units could be seen moving towards the Gaza border on Sunday, which indicate a ground invasion could be imminent.

However, Foreign Minister Tzipi Livni said that Israel does not intend to occupy Gaza but wants to end Gaza rocket fire for good.

"Our goal is not to reoccupy," Livni said during an interview Sunday on NBC's Meet the Press.

The latest round of violence began when Hamas refused to stop firing rockets into Israel from the Gaza Strip, despite repeated threats of an air strike. Israel retaliated, destroying dozens of Hamas security compounds. But Gaza is one of the most densely-populated areas on the planet, and the attacks left an unknown number of civilians dead.

The Palestinian Centre for Human Rights reported on Sunday that at least 20 of the dead were children under 16 and nine were women. The group says it keeps researchers at all Gaza Strip hospitals.

On Sunday, Israeli aircraft dropped bombs and missiles on a number of targets, including a tanker truck, a medicine supply warehouse, a mosque and a television station.

Four people were killed and 25 wounded in an attack on one of Gaza City's key security compounds.

After the attack, Hamas police placed the organization's green flag in the rubble.

"These strikes fuel our popular support, our military power and the firmness of our positions," Mushir al-Masri, a Hamas legislator, said. "We will survive, we will move forward, we will not surrender, we will not be shaken."

In the first 24 hours of the campaign, which began around midday Saturday, the air strike count was at 250.

Israel claimed that Palestinian militants have fired more than 300 rockets and mortars into Israel during the last week, but an Israeli official noted Sunday that Hamas' ability to fire rockets had been reduced by 50 per cent.

Palestinian militants launched about 20 rockets and mortars into Israel after the strikes began.

Two rockets hit close to southern Israel's largest city, Ashdod, which is about 38 kilometres from Gaza. That is the farthest a rocket fired from Gaza has ever reached in Israel.

Palestinian President Mahmoud Abbas, a political moderate who is a rival to Hamas -- the party that controls Gaza -- has called on the group to revive talks with Israel and re-establish a truce that had been established early last spring.

The United States was just one of Israel's key allies to call for restraint on Sunday.

U.S. Ambassador Zalmay Khalilzad, Israel's closest ally on the U.N. Security Council, said "the key issue here was not to point a finger at Israel. The key issue was to urge all parties to end the violence and address the humanitarian needs of the people of Gaza."

After the plea to open Gaza's border to humanitarian supplies, Israeli Defence Minister Ehud Barak allowed some fuel and medicine to enter the region.

Among the confirmed civilian deaths on Sunday was a 15-year-old boy, who was killed in southern Gaza after an attack on a greenhouse.

Gaza City streets were largely empty on Sunday, as most residents chose to stay in hiding. Schools were closed for a three-day mourning period for those killed in the attacks.

With files from The Associated Press