The dispute over the tanks’ entry into Sinai earlier this month appeared to be part of a delicate balancing act as Egypt’s new leadership, which is interested in changing the terms of the military aspects of the treaty, tests Israel’s limits. For its part, Israel seeks to encourage Egypt’s efforts to restore order in the increasingly chaotic Sinai Peninsula but without posing a threat to its own security.

With Egyptian forces in Sinai strictly limited by the military appendix of the peace treaty, the vast desert area has until now served as a demilitarized buffer zone. But Egypt has long chafed at the restrictions, contending that restoring security in Sinai, which is a joint Israeli-Egyptian interest after all, requires additional forces and heavier weaponry.

“It is clear to everyone that the Egyptians — whether they succeed in dealing with the terror in Sinai or don’t — at some point are going to ask to open the military appendix,” Alex Fishman, a military affairs analyst, wrote Tuesday in Yediot Aharonot, a popular newspaper. “The meaning of this is that the demilitarization of Sinai will be eroded, which is one of the most important anchors of the peace agreement between Israel and Egypt.”

Long bound by a so-called cold peace, the atmosphere between the two countries has grown chillier since the election of Mr. Morsi, a former leader of the Muslim Brotherhood. Adding to the uncertainty, Mr. Morsi forced out leading members of the military old guard this month, including many of the faces most familiar to Israel, in a move to regain political power that the military seized after the revolution last year.

The purge came soon after a brazen Aug. 5 attack by gunmen who opened fire on an Egyptian Army checkpoint in the northern Sinai Peninsula, killing 16 soldiers. The gunmen then exploded a truck packed with explosives at the border fence with Israel and drove an armored vehicle, also loaded with explosives, about a mile into Israel before Israeli airstrikes destroyed it.