For the first time, the warning included the ancient port city’s Christian quarter, underscoring how Israel’s offensive was widening. Many residents have fled Tyre since the war began, leaving the Christian quarter as one of the city’s last relatively populated enclaves.

The Israeli military said last week that it had “identified activity by dozens of Hezbollah operatives inside the Christian neighborhood,” and called on residents “to demand the removal of the organization’s operatives from your areas.” It provided no evidence for its claim.

Israeli strikes on Tuesday also targeted towns and villages across southern Lebanon, including areas that were not covered by evacuation warnings, according to Lebanon’s state-run news agency.

The enduring conflict in Lebanon has become one of the central obstacles in President Trump’s efforts to reach an agreement to end the U.S.-Israeli war with Iran. For weeks, Tehran has insisted that any deal include an end to the fighting in Lebanon, but Israel has rejected efforts to connect the two conflicts.

Israel and Lebanon agreed last week to a new cease-fire following talks in Washington.

But Hezbollah, which was not a party to the discussions, rejected the proposal because it required the group to stop firing without any immediate concessions from Israel. With the Lebanese government unable to compel the powerful armed group to abide by any truce, the cease-fire announcement has had little effect.

On Sunday, an Israeli strike on the Dahiya neighborhood on the southern outskirts of Beirut, where Hezbollah holds sway, prompted Iran and Israel to launch strikes against each other for the first time since a fragile truce took effect in April.

Iran has since threatened to attack Israel again if it keeps up its offensive, including in southern Lebanon.

Tyre, a UNESCO World Heritage Site, is one of southern Lebanon’s largest cities and renowned for its spectacular Roman ruins. The evacuation warning, which ordered residents to flee more than 15 miles to the north, prompted a new wave of displacement from the city.

Emergency shelters quickly filled up, and rescue teams worked to evacuate older residents as panic spread through the city’s streets, according to the Lebanese authorities.

“You can’t ask 100,000 people residing in Tyre to leave at once,” said the city’s mayor, Hassan Dbouk, who remained in the city despite the Israeli warning.

“Some people decided to stay simply because they have no place to flee,” he added.

The sweeping Israeli evacuation warning on Tuesday included the city’s Christian quarter, which has long been seen as a haven in wars. During repeated bouts of conflict between Israel and Hezbollah in recent decades, residents from other parts of the city had often sheltered in the neighborhood’s harbor-side alleyways, an area that was once a favorite weekend destination for Lebanese.

Since Hezbollah fired rockets into Israel in March, triggering Israel’s latest offensive, the neighborhood had been spared the airstrikes that pummeled the rest of the city.

As the fighting continued, the Israeli military said it had killed a gunman who had crossed into Israeli territory from Lebanon and opened fire at soldiers near the border. The rare incident led authorities to instruct residents of two Israeli border villages to shelter in place, according to a spokesman for the local regional council.

The Israeli military said the incident was “under review,” and did not immediately identify the gunman’s affiliation with any armed group.

Gabby Sobelman, Hwaida Saad and Johnatan Reiss reporting.