JERUSALEM — Efforts to agree on a cease-fire between Israel and Hamas intensified Tuesday, but the struggle to achieve even a brief pause in the fighting emphasized the obstacles to finding any lasting solution.

On the deadliest day of fighting in the week-old conflict, Secretary of State Hillary Rodham Clinton arrived hurriedly in Jerusalem and met with Prime Minister Benjamin Netanyahu of Israel to push for a truce. She was due in Cairo on Wednesday to consult with Egyptian officials in contact with Hamas, placing her and the Obama administration at the center of a fraught process with multiple parties, interests and demands.

Officials on all sides had raised expectations that a cease-fire would begin around midnight, followed by negotiations for a longer-term agreement. But by the end of Tuesday, officials with Hamas, the militant Islamist group that governs Gaza, said any announcement would not come at least until Wednesday.