He says that "the elements of an agreement" for a cease-fire "are there," adding that they are being worked on "very hard."
Blair is the Middle East envoy for the U.S., EU, Russia and the U.N., the four countries known as the Quartet supervising the Middle East peace process.
He says that any plan to end fighting must also halt weapons smuggling to Hamas and open Gaza's borders.
Israel attacked the Gaza Strip on Dec. 27 to end rocket fire by Hamas. Some 870 Palestinians have died so far.