Kerry was not specific Wednesday in describing what he called steps forward in the negotiations as he met for a second time this week with United Nations chief Ban Ki-moon.
Both Kerry and Ban are in the Mideast trying to broker a new truce between Israel and Hamas, which controls Gaza.
More than 630 Palestinians and about 30 Israelis have been killed in most recent round of violence that began July 8.
Kerry flew into Israel's main airport Wednesday despite a Federal Aviation Administration ban put in place a day earlier after a Hamas rocket landed nearby.
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