"It is of critical importance that the ceasefire be extended and consolidated," George Mitchell said.
Mitchell, who arrived in Israel earlier on Wednesday, has met with Prime Minister Ehud Olmert and President Shimon Peres, and is due to meet with Palestinian President Mahmoud Abbas in the West Bank on Thursday.
Olmert told the U.S. envoy that opening the Gaza crossings was linked to "solving the issue of captured IDF soldier Gilad Schalit" and that until a solution was found, "the crossings will be opened for humanitarian aid only, out of concern and consideration for the needs of the Gazan population."
Over 1,300 Palestinians were killed during Israel's more than three week long military operation in the Gaza Strip. Israel said Operation Cast Lead was aimed at stopping rocket and mortar fire from Gaza toward south Israel.
A truce was announced January 18. However, violence has recently flared up on the Israeli-Gaza border.