After a 6 a.m. deadline passed, a spokesman for the shadowy Army of Islam said the groups holding Shalit "have decided to freeze all contacts and close the files of this soldier."
The previously unknown Army of Islam was among three groups that took part in the June 25 cross-border raid that killed two Israeli soldiers and abducted Shalit, 19. Two other groups, the military wing of the ruling Hamas party and the Hamas-linked Popular Resistance Committees, also claimed responsibility.
Since the abduction, the militants have called on Israel to release hundreds of prisoners in exchange for information about Shalit. The abductors have given no concrete information about the soldier's condition, though Israeli officials believe he is alive.
Israeli Prime Minister Ehud Olmert has rejected any negotiations with the militants, and last week launched a ground invasion in the Gaza Strip aimed at pressuring the Hamas-led Palestinian government to secure the soldier's release.
Cabinet minister Roni Bar-On, who is close to Olmert, said there was no change in the Israeli position after Tuesday's deadline passed. "Israel will not give in to terrorists and will not give in to extortion," he told Israel Radio.
Despite the tough public line, Israeli officials have privately said they would consider other options to get the soldier back. Israel has released prisoners before in lopsided exchanges for captured citizens or the dead bodies of soldiers killed in battle.
Egypt has been leading international mediation efforts to solve the crisis, including talking to Syria, whose president, Bashar Assad, is believed to hold influence over Hamas' Syria-based political head, Khaled Mashaal.
Hamas sent out mixed messages late Monday. In Gaza, government spokesman Ghazi Hamad expressed hope for a diplomatic solution.
But Osama Hamdan, one of the most senior members of the exiled Hamas leadership, ruled out a compromise and threatened to abduct more Israelis.