There have been efforts by UN and Egyptian officials to secure a long-term truce between Israel and Hamas, although Israeli officials have not commented on it.
Since July, there have been three major outbreaks of violence.
"We are in the midst of a campaign against terror in Gaza," Netanyahu said at the start of a cabinet meeting. "It will not end at once.
"Our demand is clear: a total ceasefire, we will not settle for anything less than that," he added.
"So far we have destroyed hundreds of Hamas military targets and with each round of attacks, the Israel Defense Forces charge Hamas another high price."
Netanyahu has been under political pressure to act more forcefully against Hamas, although both sides are reluctant to start a fourth war between them since 2008.
Israel has also sought an end to the kites and balloons that carry firebombs over Gaza's border fence to burn Israeli farmland.
An informal truce reached on Thursday night has been maintained despite the death of three Palestinians since Israeli army fire during border protests and clashes.
On Thursday there were extensive Israeli air strikes in retaliation for the launch of more than 180 rockets and mortar shells by Hamas and its allies as of Wednesday night.
Three Palestinians were killed in the Israeli attacks, including one mother and her 18-month-old daughter, while seven Israelis were wounded by Palestinian rocket fire while hundreds fled to the air-raid shelters.
It was one of the most serious escalations since the Gaza war of 2014 and followed months of growing tensions.
At least 168 Palestinians have been killed since protests on the Gaza border and clashes began on March 30, with most succumbing to Israeli fire during the demonstrations. Others have died in air attacks.
In the same period, a Palestinian sniper shot and killed an Israeli soldier.