The three-stage ceasefire which came into effect on January 19 is now nearing the end of its first phase.
It has largely held despite accusations of violations by both sides and a series of setbacks, the latest of which came over the weekend.
"We have to get an extension of phase one. I'll be going to the region this week, probably Wednesday, to negotiate that and we are hopeful that we have the proper time to begin phase two and finish it off and get more hostages released," Witkoff told CNN's State of the Union on Sunday.
The first phase of the ceasefire included a deal to exchange 33 Israeli hostages held in Gaza for almost 2000 Palestinian detainees and prisoners held by Israel.
The second phase would include a full withdrawal of Israeli forces from Gaza and the release of around 60 remaining hostages.
The ceasefire agreement hit a new hurdle on Saturday when Israel delayed the release of 602 Palestinians from its jails in exchange for six Israeli hostages who were led by armed militants onto a stage in front of a crowd in Gaza before being handed to the Red Cross.
Hamas-staged public handover ceremonies which have included the display of living hostages and of coffins carrying hostages' remains, have drawn increasing criticism over the past few weeks, including from the United Nations.
Israeli Prime Minister Benjamin Netanyahu said on Sunday, Israel was waiting to deliver the Palestinian prisoners and detainees "until the release of the next hostages has been assured, and without the humiliating ceremonies".
Hamas said the ceremonies were dignified and Israel was using them as a pretext to evade its obligations agreed to under the ceasefire. The bodies of four more hostages are supposed to be released by the group this week.
Meanwhile, Israeli tanks have moved into the occupied West Bank for the first time since 2002, shortly after the defence minister said troops would remain "for the coming year" in parts of the territory and indicated that Palestinians who have fled cannot return.
Associated Press journalists saw a handful of tanks move Sunday into Jenin, long a bastion of armed struggle against Israel.
Israel is deepening its crackdown on the Palestinian territory and has said it is determined to stamp out militancy amid a rise in attacks.
It launched the offensive in the northern West Bank on January 21 — two days after the current ceasefire in Gaza took hold — and expanded it to nearby areas.
Palestinians view such raids as part of an effort to cement Israeli control over the territory, where three million Palestinians live under military rule. The deadly raids have caused destruction in urban areas.
Israeli Defence Minister Israel Katz said he and Netanyahu ordered the military to "increase the intensity of the activity to thwart terrorism" in all refugee camps in the West Bank.
with AP
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