Israeli and Palestinian negotiators are understood to be trying to thrash out a deal that will see the current 72-hour truce extended.
Hamas, which controls Gaza, has suggested both sides are far from agreeing on common conditions.
The deal is due to expire on Friday morning and Israeli officials have indicated they are willing to push back the ceasefire.
Paul Hirschson, Israeli Foreign Ministry spokesman: “I think that we should look forward and see how we can do two things. On the one hand how we can demilitarize de Gaza strip, and on the other hand how we can rebuild and bring a better life to the people of Gaza and the relationship between ourselves and them.”
Nearly 2,000 people have been killed during four weeks of fierce fighting between Israeli forces and militants in Gaza.