"Now we're talking about a permanent easing," said Maj. Guy Inbar, a military spokesman. "The longer the calm persists, the more we'll weigh additional easing of restrictions that will benefit the private sector."
Hamas downplayed the move, calling it inadequate. Gaza economists said it would take years of shipments to make a dent in the gap left by the five years of blockade.
Inbar said 20 truckloads a day could enter Gaza, and other concessions may follow "depending on the continuation of the calm."
Last week, Israel authorized the entry of 60 trucks and buses for the first time since the Hamas takeover.
Gaza crossing official Raed Fattouh confirmed that Israeli agreed to send in 20 trucks of gravel daily, five days a week.
"The Israelis promised to undertake further measures to alleviate the difficult economic situation in Gaza as a result of the calm," he said. "This move had been expected as part of the deal."
Gaza's leaders demand much more. Hamas wants Israel to lift the remainder of the blockade and the lifting of a near-total ban on exports from the impoverished territory. Exports, especially to the West Bank, the Palestinian territory on the opposite side of Israel, once formed the backbone of Gaza's economy. The West Bank is run by the more moderate Fatah, ousted from Gaza by Hamas.
Critics contend the export ban punishes ordinary Gazans instead of pressuring Hamas, contributing heavily to an unemployment rate of about one-third of the workforce. Eighty percent of Gaza's 1.6 million people rely on U.N. support.
Egypt eased its own restrictions on Saturday, allowing in 1,400 tons of gravel paid for by Qatar. The oil-rich emirate pledged $425 million to build housing, schools, a hospital and roads in Gaza as part of its attempt to build its influence in Palestinian politics and its power in the region, at the expense of regional rival Iran, Hamas' longtime patron.