Yair Lapid writes in a statement on X that Israel should participate in the discussions with Hamas and US President Donald Trump to get the hostages released and an end to the war.
"I have informed the American administration that Netanyahu has backing at home to continue the process," writes Lapid.
This means that Netanyahu could remain as prime minister even if parts of his coalition, which want to see continued war in Gaza, were to leave the government.
Many reactions
Several positive reactions have come since Hamas opened up for discussions about peace.
The mediating countries Qatar and Egypt have taken a positive stance on Trump's peace plan and welcome Hamas' statement.
French President Emmanuel Macron writes on X that the release of hostages and a ceasefire are "within reach".
"We now have the opportunity to take decisive steps towards peace," he writes.
UN Secretary-General Antonio Guterres announces through a spokesperson that he welcomes Hamas' statement.
"He urges all parties to take the opportunity to end the tragic conflict in Gaza," the statement says.
Hamas statement
Hamas stated in a statement on Friday that it is ready to release all hostages in Gaza within the framework of the US proposal for a ceasefire.
But the terrorist-stamped group also says it wants to initiate negotiations through mediators on "the details of the agreement".
Hamas points out that an agreement must "achieve an end to the war and a complete withdrawal from the strip" (of Israeli forces). The group also says it is ready to hand over control of the Gaza Strip to an independent Palestinian technocratic transitional government, based on "Palestinian national consensus and with Arab and Islamic support".
Hamas does not mention its own disarmament, which is a requirement in the proposal.