Aircraft struck three training facilities of Hamas's military wing, the Ezzedine al-Qassam Brigades, around the coastal territory, but caused no casualties, medics and eyewitnesses said.
They also hit buildings in Gaza City, Deir el-Balah in the southern part of the strip, and in the northern town of Jabaliya, injuring an unspecified number of people.
There was shelling reported in Beit Lahiya, in the far north of the strip, where Israel had earlier warned residents of an impending assault.
Israel also moved against Hamas in the occupied West Bank, arresting five of the movement's lawmakers in Nablus and Jenin, Palestinian security officials told AFP.
UN chief Ban Ki-moon said "too many" Palestinian civilians have been killed, as the Palestinian death toll from the punishing Israeli campaign hit 172 with another 1,230 people wounded.
Ban also urged Israel to scrap plans for a potentially devastating ground offensive, fears of which have sent Gazans fleeing from the north.
Read: Israel steps up Gaza campaign, thousands flee
Palestinians mourn their relatives in the morgue of the Shifa hospital in Gaza City. Over a dozen Palestinians were killed in an Israeli strike on a house, hospital officials said. (AP photo)
About 17,000 people have taken shelter in installations of the UN agency for Palestinian refugees, UNRWA, the agency said in a statement.
Israeli media reported that a security cabinet meeting ended late Sunday with no orders for a ground assault.
But despite increasing calls for a ceasefire, Israeli Prime Minister Benjamin Netanyahu said the military was hitting Hamas "with growing force", warning there was no end in sight.
"We do not know when this operation will end," he told ministers.
US Secretary of State John Kerry phoned Netanyahu to renew a US offer to help mediate a truce and he "highlighted the US concern about escalating tensions on the ground," a senior State Department official said.
Kerry also said that he was engaged with regional leaders "to help to stop the rocket fire so calm can be restored and civilian casualties prevented".
Palestinian president Mahmud Abbas said he would ask Ban to "put the State of Palestine under the UN international protection system" in order to address the violence in Gaza.
As the death toll rose, the Gaza-based Palestinian Centre for Human Rights said most of the victims were civilians, putting their number at more than 130, among them 35 children and 26 women.
It also said Israel had hit 147 homes and badly damaged hundreds of others.
So far, no Israelis have been killed, although militants in Gaza have pounded the south and centre of the country with about 715 rockets since the fighting began on July 8, an army spokeswoman told AFP late Sunday. Around 160 had been intercepted, she said.
Israeli residents stand on a hill overlooking the Gaza Strip to watch the fighting between the Israeli army and Palestinian militants. (AFP photo)
Rocket fire from Syria, Lebanon
For the first time during the Israeli operation, a rocket fired from Syria hit the Israeli-occupied sector of the Golan heights but landed on empty ground, causing no casualties.
Israel responded with artillery fire at Syrian army positions, the Israeli military said.
Four rockets fired from southern Lebanon struck northern Israel early Monday, Lebanese security sources said.
No casualties were reported in Israel and the army responded with artillery fire.
An AFP correspondent in southern Lebanon reported more than 30 shells were fired, but there was no information yet on casualties.
Early Sunday, Israeli naval commandos staged a brief ground assault in northern Gaza on a mission to destroy longer-range rockets, with the army warning residents to leave the area ahead of a major assault on the sector.
Hamas told Gazans to ignore the Israeli warnings.
Speaking on condition of anonymity, a senior Israeli military official said the area was rife with rocket launchers and would be targeted further.
A picture taken from the southern Israeli Gaza border shows rockets being fired from the Gaza strip into Israel. (AFP photo)
Thousands of Gazans flee
In northern Gaza, even before the army's warnings went out, thousands of residents of the blockaded coastal strip began fleeing the traumatic violence, an AFP correspondent reported.
"It was the middle of the night, and I gathered the children, they were so afraid," said Samari al-Atar, breaking down in tears as she described how her family fled barefoot with shooting all around.
Saturday's death toll was the highest yet with 56 people killed, including 18 people who died in a single strike on a house in Gaza City, medics said.
Eight people were killed in air strikes on Sunday and another two died early Monday of injuries received in earlier raids.
Pope Francis appealed to world leaders for both prayer and diplomacy to halt the bloodshed, while the German and Italian foreign ministers were both poised to head to the region to join truce efforts, their offices said.
Read: Pope appeals for peace in Gaza conflict
With Palestinian civilians bearing the brunt of the violence, clashes erupted in central Paris as thousands of people protested against Israel and in support of Gazans. Protesters also rallied across Asia to condemn the Israeli offensive, with 3,000 gathering in Sydney and hundreds more in Hong Kong, New Delhi and Jakarta.
Israeli soldiers from the Nahal Infantry Brigade walk across a field near central Gaza Strip. (Reuters photo)
No rush into land assault
Israel has warned that preparations are under way for a possible ground incursion.
But Israeli media said that a meeting of Netanyahu's security cabinet ended Sunday night without giving the order for ground operations.
The latest escalation began on June 12 when three Israeli teenagers were kidnapped and murdered, triggering a crackdown on Hamas in the West Bank and an uptick of rocket fire from Gaza, which worsened after a Palestinian teen was killed by Jewish extremists on July 2.