Israeli Defense Minister Moshe Yaalon said ground operations in Gaza could soon be broadened “significantly”.
John Kerry said he still hoped for an initial seven-day truce for next week’s Eid festival but there was “still some terminology… to work through”.
He said he was confident Israeli PM Benjamin Netanyahu was committed to finding a solution.
Israel and the Islamist group Hamas have been fighting for 18 days.
Israel’s Channel 1 TV reported that the cabinet had unanimously rejected the truce proposal “as it stands”.
More than 800 Palestinians, mostly civilians, and 36 Israelis have died since the start of the conflict.
Hamas is yet to respond to the proposed ceasefire but its leader has already said the group will not agree to a deal without an end to Israel’s blockade of the Gaza Strip.
Israeli airstrikes on Gaza continued on Friday. The Israel Defense Forces (IDF) said it had killed a senior member of the militant group Islamic Jihad.
The IDF also said its Iron Dome defense system had intercepted several rockets fired across the border by Hamas.
Israel launched its military offensive on July 8 with the declared objective of stopping Hamas firing rockets into Israel.
It has since extended its operation to destroy tunnels dug by militants to infiltrate Israel.
Rioting has erupted for the second night running at the Qalandia checkpoint in the West Bank, where 10,000 protesters massed on Thursday, clashing with Israeli border police.
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