Secretary of State Antony Blinken will travel to Egypt this week to discuss efforts to reach a Gaza cease-fire and hostage release deal, the State Department said.

Blinken will travel to Egypt Wednesday through Friday to co-chair the opening of the U.S.-Egypt Strategic Dialogue with Egyptian Foreign Minister Badr Abdelatty, the department said.

He will also meet with Egyptian officials "to discuss ongoing efforts to reach a ceasefire in Gaza that secures the release of all hostages, alleviates the suffering of the Palestinian people, and helps establish broader regional security," the State Department said in a statement.

-ABC News' Shannon K. Kingston

State Department spokesperson Matt Miller declined to predict when a new Gaza cease-fire and hostage release deal proposal might be ready.

"We continue to engage with our partners in the region, most specifically with Egypt and Qatar, about what that proposal will contain, and making sure -- or trying to see that it’s a proposal that can get the parties to an ultimate agreement," Miller told reporters Monday.

"I don't have a timetable for you other than to say that we are working expeditiously to try to develop that proposal, try to find something that would bring both the parties to say yes and to formally submit it," Miller added

Secretary of State Antony Blinken had previously said more than a week ago that a proposal would be presented to both Israel and Hamas "in the coming days."

Miller said Monday that -- just like in the negotiations overall -- the main hurdles for creating the new proposal were the security situation in the Philadelphi corridor and the number of hostages and Palestinian prisoners that would be released.

-ABC News' Shannon K. Kingston

Time is running out for a diplomatic solution to the ongoing conflict at the Israel-Lebanon border, Israeli Defense Minister Yoav Gallant told Secretary of Defense Lloyd Austin in an overnight phone call.

"Hezbollah continues to 'tie itself' to Hamas -- the trajectory is clear," Gallant told Austin per a readout from the Israeli Defense Ministry.

Gallant "reiterated Israel's commitment to the removal of Hezbollah presence in southern Lebanon, and to enabling the safe return of Israel's northern communities to their homes," the defense ministry said.

Cross-border fighting between the Israel Defense Forces and Hezbollah -- which is aligned with Iran and Hamas through the so-called "Axis of Resistance" -- has been near-constant since Oct. 8.

Tens of thousands of Israelis have left their homes in the north of the country amid the fighting, with Israeli leaders repeatedly threatening a significant military operation to pacify Hezbollah forces operating in southern Lebanon.

Prime Minister Benjamin Netanyahu said in a Sunday statement that the "current situation will not continue. This requires a change in the balance of forces on our northern border. We will do whatever is necessary to return our residents securely to their homes."

-ABC News' Jordana Miller

A missile described by the Houthis as a "new hypersonic ballistic missile” was hit by an Israeli interceptor, Israeli military officials said Sunday, after initially saying it got through its defenses and fell in an open area.

An Israeli interceptor hit the missile fired into central Israel from Yemen, causing it to fragment, according to Israeli officials. The missile was not destroyed, but caused no damage, the Israeli officials said.

"The conclusion into the review of the surface-to-surface missile that was fired this morning is that there was a hit on the target from an interceptor, as a result of which the target fragmented but was not destroyed," an Israeli military official said in a statement.

The Houthi movement claimed responsibility for the missile attack, claiming in a statement that it was aimed at an "important military target" in the Tel Aviv region. The Houthis claimed the missile flew some 1,267 miles in less than 12 minutes and that Israeli anti-missile defenses "failed to intercept" the weapon.

The Israel Defense Forces initially confirmed to ABC News that its defenses failed to intercept the missile but changed its conclusions upon further investigation.

-ABC News' Victoria Beaule