Deadly clashes between Israeli troops and Hamas fighters over the past 48 hours have put their six-month-old ceasefire under severe strain.
Both Israel and Hamas have accused each other of violating the truce.
The violent clashes on Tuesday and Wednesday were the most serious since the two sides agreed on the ceasefire on June 19.
Seven Palestinians were killed in fighting that erupted after Israeli soldiers raided the Gaza Strip to purportedly destory a tunnel.
Ayman Mohyeldin, Al Jazeera's correspondent reporting from Gaza, said: "Both the Palestinians and the Israelis are putting great emphasis on the ceasefire being extrememly fragile at this stage.
The last two days of attacks also come on the eve of Egyptian mediated talks aimed at reconciling Palestinian factions … but with some of them already sceptical about the truce, the latest violence could deepen divisions about what is the best way forward for Palestinians trying to end a siege," he said.
Israel said on Thursday it favoured an extension of the truce in Gaza, which is controlled by Hamas, despite the recent clashes.
"We hope the truce can again be applied, we believe in this truce and it looks like things are calming down," Matan Vilnai, the Israeli deputy defence minister, said.
Fawzi Barhum, a Hamas spokesman, said an extension of the truce agreement "would not prevent the resistance from responding to violations by the occupation."
The tensions came amid a visit to the region by Condoleezza Rice, the US secretary of state. Rice is scheduled to hold talks with Israeli officials and Palestinian Authority officials in the West Bank to define the outlines of a peace deal.
Rice is making her eighth trip to the region since the November 2007 Annapolis peace conference which launched the US initiative.