Egyptian mediators have been racing to bridge gaps between Palestinians and Israelis as they struggle to secure a lasting Gaza truce before the midnight expiry of a three-day ceasefire.
Egypt brokered the 72-hour truce which took effect at 00:01 on Monday (2101 GMT Sunday), and has urged the Israelis and Hamas, to make every effort to reach a permanent ceasefire
A Palestinian official said on Wednesday that the indirect talks, held at the General Intelligence headquarters in Cairo, were expected to go down to the wire.
On Wednesday, Israeli police said a rocket from Gaza had landed in southern Israeli, hours before the truce was supposed to come to an end, the Reuters news agency reported.
Hamas denied firing any rockets in to Israel.
By the time the deadline passes, the two sides must have either agreed on a permanent ceasefire, accepted an extension or risk a resumption of more than a month of bloody fighting.
Mediators have proposed that talks on key Palestinian demands of a seaport and an airport in Gaza be delayed until a month after a permanent ceasefire takes effect, according to the Egyptian proposal contained in documents, the AFP news agency said.
Negotiations on proposals for the handover of the bodies of two slain Israeli soldiers held by Palestinian armed groups in exchange for the release of prisoners in Israeli jails would also be postponed, according to the document.
Under the proposal, the buffer zone along Gaza's border with Israel would be gradually reduced and guarded by Palestinian President Mahmoud Abbas's security teams.
The negotiations "are in a very sensitive stage and we hope to reach an agreement" before midnight (2100 GMT), said Palestinian delegation head Azzam al-Ahmed.
Hamas is understood to be demanding clear commitments to opening the ports in Gaza, even if they are to be established at a later date.
The Palestinians are also demanding an end to the eight-year blockade of Gaza.
The document was vague on the blockade, saying the crossings would be opened according to agreements reached between the Palestinian Authority and Israel.
The Palestinians, for their part, have rejected an Israeli demand for Hamas and other armed groups in Gaza to disarm.
Nearly 2,000 Palestinians have been killed since Israel launched its Gaza offensive on July 8 to halt cross-border rocket fire. On the Israeli side, 67 people have been killed, 64 of them soldiers.