"What is coming will be worse," the Israeli military said in phone messages targeting Gaza militants.
Israeli leaders have been mulling whether to expand the assault against Hamas in Gaza, or respond to international calls for a truce.
The international community so far has been unable to bring about a cease-fire that would end the fighting, which has already killed at least 1,050 Palestinians, 52 Israeli soldiers and three civilians on the Israeli side.
But with attacks mounting from both sides Monday, and Israel and Hamas far apart on terms for a truce, a cease-fire appeared elusive.
"We need to be ready for a prolonged campaign," Israeli Prime Minister Benjamin Netanyahu said, standing beside his defense minister and chief of staff. "We will continue to act aggressively and responsibly until the mission is completed to protect our citizens, soldiers and children."
Hamas spokesman Sami Abu Zuhri struck a defiant tone in response to Netanyahu's warnings.
"His threats do not scare Hamas or the Palestinian people and the occupation will pay the price for the massacres against civilians and children," he said.
Israel said it sent text messages and phoned residents of northern Gaza — including Shijaiyah, the site of one of the war's bloodiest battles last week — urging them to flee their homes and move toward Gaza City.
The United Nations on Monday called for an "immediate" cease-fire in the fighting and on Sunday, President Barack Obama called Netanyahu to push for an immediate end to the conflict.
But Israel and Hamas' terms for ending the fighting remain far apart. Hamas has conditioned a halt to the fighting on an easing of a crippling blockade on the territory imposed by Egypt and Israel.
Israel meanwhile wants to see the Gaza Strip demilitarized and Hamas stripped of its rocket firing abilities.
Israel says it launched its war on July 8 to halt incessant rocket fire from Gaza. It later broadened the assault into a ground offensive meant to tackle Hamas' network of tunnels which Israel sees as a major threat.
Despite Israel's attempts to destroy the tunnels, the Israeli military said Monday that militants succeeded to enter Israel through a tunnel leading from Gaza, a sign that the threat of attacks from tunnels has not been eradicated. The military said troops killed one militant.
Also Monday, the Israeli military said that a mortar attack on southern Israel killing four soldiers. Another five soldiers were killed Monday, but the details behind their deaths were not immediately released.
Earlier, a strike on a Gaza park killed 10 people Monday, nine of them children, as Israeli and Palestinian authorities traded blame over the attack.
The Gaza park attack happened as children played on a swing in the Shati refugee camp on the edge of Gaza City, said Ayman Sahabani, head of the emergency room at nearby Shifa Hospital. Sahabani said nine of the 10 killed at the park were children under the age of 12 and 46 were wounded.
The strike occurred a few minutes after an outpatient clinic at Gaza's main hospital, Shifa, was hit, leaving several people wounded. Camera crews were prevented from filming the area of impact at Shifa.
Gaza's police operations room, Civil Defense and Sahabani blamed the attacks on Israeli airstrikes.
Lt. Col. Peter Lerner, an Israeli army spokesman, denied Israel was involved. "This incident was carried out by Gaza terrorists whose rockets fell short and hit the Shifa Hospital and the Beach (Shati) camp," he said, adding that the military had identified 200 "failed launchings."
Gaza's Interior Ministry spokesman Eyad al-Bozum said he believes that shrapnel found in dead bodies and in the wounded is evidence of Israel's role in the incident.
"The occupation claims that Palestinian rockets hit the hospital and the park," he said. "This is an attempt to cover their ugly crime against children and civilians, and because of their fear of scandal and international legal prosecution."
In some parts of Gaza, residents said they received messages to evacuate, but due to heavy tank shelling nearby, did not feel safe enough to flee. Israel said it warned residents in several areas of northern Gaza — including Shijaiyah, which saw one of the bloodiest battles last week — to leave.
Jabaliya resident Sufian Abed Rabo said his family of 17 has taken refuge underneath the stairway in the building of their home, which they rebuilt after it sustained damage during the 2009 war in Gaza.
"God help us. We have nothing to do but pray," Rabo said. "Maybe in the morning (we will evacuate), if we are still alive."
More than 170,000 people have already fled the fighting, with many seeking shelter in U.N. facilities. In previous battles, entire neighborhoods in Gaza have been flattened and turned to rubble.
Israel also resumed tank shelling along the eastern and southern parts of the Gaza Strip on Monday night, according to the Palestinian Red Crescent. At least six people were killed in tank shelling across the territory.
Goldenberg reported from Jerusalem. Associated Press writers Edith M. Lederer at the United Nations and Yousur Alhlou in Jerusalem contributed to this report.
Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.