On Monday, Netanyahu and Gantz, who serves as alternate Prime Minister and Defence Minister, held separate meetings with Avi Berkowitz, US President Donald Trump's envoy for international negotiations over the annexation plan, reports Xinhua news agency.
Netanyahu had already declared that he wants to begin imposing Israeli sovereignty over Jordan Valley, part of the West Bank, as soon as July 1, in accordance with Trump's Middle East peace plan.
But Gantz told a meeting of lawmakers with his centrist Blue and White party that "anything not related to the struggle against the coronavirus will wait".
"Before making any political moves, we need to help the public to get back to earn a living with dignity," Gantz said.
In the afternoon, Netanyahu was quoted as dismissing Gantz's remarks.
He told a meeting of lawmakers with his right-wing Likud party that he is working "discretely" with envoys of Trump, his close ally.
"The issue does not depend on Blue and White," he said, according to local media reports.
Under their power-sharing deal, both Netanyahu and Gantz hold veto power over key government decisions.
However, the deal allows Netanyahu to bring an annexation proposal to the cabinet starting from July 1, even without Gantz approval.
The annexation plan was accepted with widespread condemnations by the Palestinians, most of the Arab world, and the international community.
UN High Commissioner for Human Rights Michelle Bachelet urged Israel on Monday to halt the "illegal" plan.
"I am deeply concerned that even the most minimalist form of annexation would lead to increased violence and loss of life, as walls are erected, security forces deployed and the two populations brought into closer proximity," Bachelet said in a statement.
Israel captured the West Bank in the 1967 Middle East war and has controlled the territory ever since, despite international criticism.