Missile defences intercepted more than 100 rockets from Gaza and most others fell in open areas, though some hit houses and other civilian structures, the military said.
The Palestinian Ministry of Health in the Gaza Strip confirmed that the death toll of Palestinians since the start of Israeli escalation against Gaza has mounted to six people, while dozens were also injured.
Russia, Jordan and an Egyptian delegation all declared Monday that Israel is responsible for the violence in Gaza. Just last week, Israel let a Qatari plane land with cash for Gaza, meant to ease the area's distress.
Three Palestinian gunmen were killed in the air attacks.
An Israeli colonel, one Hamas commander and six others were killed in the incident.
Hamas' armed wing, the Ezzedine Al-Qassam Brigades, said the Israeli special forces team had infiltrated near Khan Yunis in the southern Gaza Strip in a civilian vehicle.
Search intensifies for victims of California's deadliest wildfire - global
It was 35% contained as of Wednesday evening, according to California Department of Forestry and Fire Protection officials. More than 5,000 personnel are fighting the blaze , which has destroyed more than 6,500 homes and 260 commercial buildings.
Netanyahu has come under attack at home for allowing the Qatari funds to flow into Gaza, with the photos of cash-stuffed suitcases leading critics to say Israel is paying protection money to Hamas in hopes of achieving quiet. Hamas has threatened to extend the range of its rocket fire.
The warning was issued on Tuesday, hours after a rocket fired from Gaza killed an Israeli man in a direct hit on a residential building in the coastal town of Ashkelon.
Israeli Prime Minister Benjamin Netanyahu cut short a visit to Paris because of the flare-up and returned to Israel on Monday for consultations with top security officials. "The United Nations Special Coordinator, Nickolay Mladenov, is working closely with Egypt and all concerned parties to restore calm", Farhan Haq, the deputy spokesman for Guterres, said in a statement.
Israel had stressed its covert operation on Sunday was an intelligence-gathering mission and "not an assassination or abduction", but Hamas strongly denounced it and vowed revenge.
A funeral was held for the seven Palestinian militants on Monday, attended by thousands, including masked Al-Qassam members carrying rifles, some firing into the air.
Tel Aviv's air strikes killed at least seven Palestinians in what appeared to be a targeted hit near the city of Khan Younis in southern Gaza near the border with Israel on Sunday. Reports also said that an Israeli officer was also killed during the ensuing clashes. Qassam members discovered the vehicle and chased it, prompting Israeli airstrikes that killed several people, the group said.