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

On Sunday, the Israel Defense Forces released the results of its investigation into the circumstances surrounding the deaths of three hostages, whose bodies were recovered from Gaza by IDF forces in December.

The three hostages -- two soldiers, Ron Sherman and Nik Beizer, and civilian Elia Toledano -- were killed "as a byproduct" of an Israeli airstrike on the compound where they were being held, according to the investigation. The IDF said the strike was targeting a Hamas commander, and that they believed the hostages were being held elsewhere.

"The findings of the investigation suggest a high probability that the three were killed as a result of a byproduct of an IDF airstrike, during the elimination of the Hamas Northern Brigade commander, Ahmed Ghandour, on November 10th, 2023," the IDF said Sunday in a statement.

-ABC News’ Jordana Miller

Israeli Prime Minister Benjamin Netanyahu vowed to retaliate against the Houthi movement after a missile fired from Yemen fell in central Israel on Sunday morning.

"This morning, the Houthis launched a surface-to-surface missile from Yemen at our territory," Netanyahu said before a cabinet meeting. "They should know that we exact a high price for any attempt to attack us."

"Whoever needs a reminder of this, is invited to visit the port of Hodeidah," the prime minister added, referring to Israel's bombing of the strategic Yemeni port in July after a Houthi drone strike killed one person in Tel Aviv.

"Whoever attacks us will not evade our strike," Netanyahu said.

-ABC News' Jordana Miller