Israel and Hamas continue indirect talks in Cairo on Thursday, with less than a day remaining before the expiration of a 72-hour cease-fire in the Gaza Strip.
Both sides appeared to be far apart on the issues, but have suggested they are willing to extend the humanitarian truce, which ended four weeks of fighting.
Israeli officials have said they are willing to extend the cease-fire unilaterally, but Hamas representatives have denied that any agreement is in place.
Speaking Wednesday at a summit of African leaders in Washington, U.S. President Barack Obama threw his support behind the Egypt-brokered talks, saying it is important to find a more sustainable solution.
Mr. Obama repeated his position that Israel has a right to defend itself from Hamas rockets and cross-border tunnels. He also said he has "no sympathy" for Hamas, which the U.S. and Israel regard as a terror group.
Hamas is seeking an end to a longstanding Israeli and Egyptian blockade that has led to widespread unemployment, forced a majority of Gazans to rely on food aid, and kept them from traveling outside the enclave.
Israel says it will not loosen its restrictions on Gaza unless it receives assurances that Hamas is disarmed and unable to import weapons.