The Cabinet minister, Yuval Steinitz, said a further extension of the humanitarian truce would be considered when the Israeli Security Cabinet meets later Saturday, after the end of the Jewish Sabbath.
In Paris, U.S. Secretary of State John Kerry met with European foreign ministers to find ways of building on Saturday's lull, the longest so far since Israel-Hamas fighting erupted July 8.
The top United Nations envoy to the Middle East, Robert Serry, urged the sides to halt their fire for an additional 24 hours.
On Friday, Israel had rejected a proposal by Kerry and U.N. chief Ban Ki-moon to halt fire for a week and to begin talks during this period on easing the border blockade of Hamas-ruled Gaza.
Hamas has said it would not halt fire until it won guarantees that the border blockade, enforced by Israel and Egypt, would be lifted.
Under a gradual extension of a humanitarian truce, Israel would not be required to discuss new border arrangements in Gaza. It would also have a freer hand in continuing to demolish Hamas military tunnels under the Gaza-Israel border, as it has done in recent days.
A Hamas spokesman, Mushir al-Masri, speaking before the Israeli decision, said that the group would consider an extension of the truce as long as "it does not mean that we retreat from our known demands."
Meanwhile, the Palestinian death toll rose above 1,000, as an additional 132 bodies were retried from the rubble during Saturday's humanitarian truce, Palestinian health official Asraf al-Kidra said.
More than 6,000 Palestinians have been wounded in the past 19 days, hundreds of homes have been destroyed and tens of thousands of Palestinians displaced.
Israel says it is doing its utmost to prevent civilian casualties, including sending evacuation warnings to residents in targeted areas, and blames Hamas for putting civilians in harm's way.
Israel has lost 40 soldiers and two civilians. A Thai worker in Israel also has been killed.