Gantz said last month he would resign from the emergency body if Netanyahu did not approve a post-war plan for Gaza by June 8.
"I call on Benny Gantz -- do not leave the emergency government. Don't give up on unity," Netanyahu said on social media platform X.
Gantz cancelled a news conference that was scheduled for Saturday, his office said, after the Israeli military said security forces had rescued four captives alive from Gaza earlier in the day.
Without directly addressing speculations he had been planning to resign, Gantz appeared on Israeli television on Saturday evening after the captives were freed.
"Alongside the justified joy over this achievement, it should not be forgotten that all the challenges Israel is facing... have remained as they were," Gantz said.
"Therefore, I say to the prime minister and the entire leadership -- today, too, we must look responsibly at what is right and how we can continue from here."
His centrist National Union Party submitted a bill last week to dissolve the Knesset, Israel's parliament, and hold early elections.
Gantz has been seen as a favourite to form a coalition in the event that Netanyahu's government is brought down and early elections are called.
The former army chief, one of Netanyahu's main rivals before he joined the war cabinet, had said this week that returning captives from Gaza was a "priority".
The army said Noa Argamani, 26, Almog Meir Jan, 22, Andrey Kozlov, 27, and Shlomi Ziv, 41, were rescued from central Gaza's Nuseirat refugee camp on Saturday.
The four had been taken to hospital and were in "good medical condition".
The Gaza government media office said at least 210 people were killed in Israeli attacks on Nuseirat camp from which the four captives were rescued.
"The number of victims from the Israeli occupation's massacre in the Nuseirat camp has risen to 210 martyrs and more than 400 wounded," the office said in a statement.
Israel says around 116 captives are still being held in Gaza, including 41 the army says are dead.
Israel's relentless bombardment and ground invasion has killed more than 36,801 Palestinians, mostly women and children, according to Gaza health officials.
The bloodiest Gaza war erupted on October 7 after Hamas launched a surprise offensive into southern Israel.
The ensuing chaos and a frantic Israeli defence response led to 1,194 deaths, according to an AFP tally of Israeli official figures.
*This story was edited by Ahram Online
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