Israeli strikes on Gaza continued Monday as Prime Minister Benjamin Netanyahu said in a news conference that the military operation to “destroy tunnels of terror” would not stop until they are all dismantled.

Netanyahu also told Israelis Monday to be ready for a "prolonged" war.

“We have to be patient. We have to have resolve so we can continue the struggle against a murderous organization that seeks to destroy us,” Netanyahu said, addressing the country.

The comments preceded the Israeli forces firing a large number of flares over Gaza City. Intense shelling could also be heard.

The military warned thousands of Palestinians to flee their homes in areas around Gaza City — often a prelude to major army strikes. At least six Palestinians were killed by Israeli artillery fire at the Bureij refugee camp in the central Gaza Strip on Tuesday local time, medics said.

Al Jazeera's Imtiaz Tyab, reporting from Gaza as missiles hit the territory, said that many people there believed the onslaught to be the heaviest since Israel's operation began three weeks ago.

"One can only imagine what this city will look like when the sun rises," he said.

Tyab said that among the buildings hit in the assault were the home of Hamas leader, Ismail Haniya, and the headquarters of the Hamas-affiliated Al Aqsa TV station, which is in a building that houses other media organizations.

An Israeli military spokeswoman had no information on the report. Haniyeh's son confirmed the strike on his Facebook page and added that the house of the former Hamas Gaza prime minister was empty.

Hamas confirmed that its TV station Al-Aqsa TV was targeted but continued to broadcast.

A number of rockets fired from Gaza were launched toward various regions in southern and central Israel, including the Tel Aviv area. At least one of the rockets was intercepted by the Iron Dome system. No casualties or damage were reported.

So far, some 1,085 Palestinians have died in the offensive, with 6,233 wounded. Israel has lost at least 53 soldiers, as well as two Israeli civilians and a Thai worker killed by rocket and mortar attacks from Gaza.

Netanyahu also indicated in his televised speech that he is widening Israel’s objectives, saying that a demilitarization of Gaza must be part of any future solution to Israel’s conflict with the territory of 1.7 million people.

The statement came as Israel and the members of the Hamas movement traded blame over who was responsible for a strike on a park in Gaza that killed 10 people, including at least eight children.

Residents blamed the park explosion, which wounded more than 40 others, on an Israeli airstrike, but Israel said a misfiring rocket launched by Hamas hit the public garden in the Shati refugee camp. Hamas has denied those allegations.

Children were playing on a swing when the strike hit the camp, on the edge of Gaza City, said Ayman Sahabani, head of the emergency room at nearby Shifa Hospital. He gave the death toll and said 46 people were also wounded. The strike on the park occurred a few minutes after the hospital’s outpatient clinic was hit, wounding several people.

Meanwhile, the Israeli military said Palestinian fighters infiltrated Israel through a tunnel under the border and opened fired on soldiers.

The clash, in which Israeli television said five gunmen were killed and Hamas said it killed 10 Israeli soldiers, appeared to wreck international hopes of turning a brief lull in fighting into a longer-term cease-fire.

There were also warnings issued by the Israeli military to civilians in three areas of Gaza — Shujayea, Zeitoun and eastern Jebaliya — to evacuate immediately. A short time later, intense shelling could be heard in northern Gaza.

Many Jebaliya residents said they did not dare attempt an escape. Sufian Abed Rabbo said his extended family of 17 had taken refuge under the stairway in their home.

"God help us. We have nothing to do but pray," the 27-year-old told The Associated Press by phone. "I don't know who left and who stayed, but in our street, we are all very scared to move."

A truce remained elusive as diplomats sought to end the fighting on the Eid al-Fitr holiday, marking the end of the Muslim holy month of Ramadan.

International pressure is mounting for Israel and Hamas to end to 21 days of shelling.

U.N. Secretary General Ban Ki-moon on Monday called for both parties to “step back from provoking or inflicting yet more tragic violence on civilians” and stressed that both the Israelis and Palestinians have a “responsibility beyond ceasing the ongoing hostilities to start a serious dialogue to address the root causes of the conflict.”

Earlier Monday, the United Nations agreed on a statement calling for both sides to implement a humanitarian truce. At an emergency meeting, the Security Council pushed for a cease-fire to extend beyond Eid al-Fitr.

The pressure for a longer-term solution comes after a 12-hour lull Saturday, agreed to by both sides after intense U.S. and U.N. mediation efforts, failed to be sustained. Israel and Hamas had endorsed calls for a 24-hour halt — but never simultaneously.

The worsening of conditions in Gaza has led to tensions between Washington and Tel Aviv. Attempts to broker an agreement by U.S. Secretary of State John Kerry — who visited the region last week in a bid to end the bloodshed, using Turkey and Qatar to mediate with Hamas — appear to have been rebuffed.

Media leaks by unnamed Israeli officials damned a draft agreement, saying Kerry was too accommodating of Hamas — a charge the U.S. has denied. Late Sunday, President Barack Obama phoned Netanyahu to further pressure the Israeli leader to hold fire unconditionally.

Al Jazeera and wire services. Nick Schifrin contributed to this report from Gaza.