Officials said that if Hamas doesn't agree to release hostages by the time Trump leaves the Middle East, the IDF will continue with its expanded invasion plan.
Trump administration's Middle East envoy, Steve Witkoff, commented at a meeting with hostage families, sources at the meeting told Channel 12.
Hamas had claimed to have lost contact with the group holding Alexander hostage following a strike on their location.
Senior US administration officials told Reuters that an agreement was reached to move forward with talks to continue working through technical elements.
Establishing ties has become especially toxic for Saudi Arabia, the birthplace of Islam, since the start of the ongoing war between Israel and Hamas.
After initial success in April, the talks in May have hit a snag. It is not clear if things can be salvaged this week.
Iran has agreed to hold a fourth round of indirect nuclear talks with the United States on Sunday in Oman.