Fighting between Israel and Hezbollah showed little sign of abating on Friday, a day after the Iran-backed militant group rejected a U.S.-brokered cease-fire, as Israeli forces bombarded towns across southern Lebanon and ordered residents to flee.

The violence and evacuation warnings have thrown into question the agreement that Israel and Lebanon announced this week after direct talks in Washington, raising doubts about whether it would ever take effect.

For many civilians in southern Lebanon, the faltering deal brought a now-familiar directive from Israel’s military to leave their homes. More than one million people have already been displaced since the latest war erupted in March, according to Lebanese authorities. Most have no indication when, or if, they can return.

The cease-fire is contingent on Hezbollah pulling back from Lebanon’s border region with Israel, and on a “complete cessation” of the group’s attacks. Israel is not required to make any immediate concessions in kind, according to the agreement, and it has said it will press on with its military offensive until those conditions are met.

Hezbollah was not involved in the negotiations for the cease-fire, and Lebanon’s government has little power to force it to comply.

The Israeli evacuation orders on Friday included the hillside town of Anqoun, which is about 16 miles from the Israeli border and within commuting distance of the Lebanese capital, Beirut.

Anqoun had previously been spared such orders, and Lebanon’s state-run news agency reported that the town was sheltering roughly 2,500 displaced people, many of whom were forced to flee again on Friday.

The latest orders came after Hezbollah’s leader, Naim Qassem, rejected the cease-fire agreement on Thursday, calling it a “humiliating” attempt to force Lebanon’s submission to Israel and tantamount to “surrender.”

Mr. Qassem said any truce deal must be comprehensive and include Israel’s withdrawal from southern Lebanon, where it has occupied broad stretches of territory since the latest invasion began in March.

“As long as the occupation continues, the resistance will continue,” Mr. Qassem said.

Israel’s defense minister, Israel Katz, gave little indication on Thursday that Israel was preparing to halt its campaign against Hezbollah. Mr. Katz said that Israeli forces would continue operating in Lebanon “at this stage,” adding that the hundreds of thousands of people displaced from southern Lebanon would not yet be allowed to return.

The ongoing fighting in Lebanon has threatened to complicate President Trump’s efforts to reach a deal with Iran, Hezbollah’s chief backer, which has threatened to pull out of peace talks if Israel does not stop attacking the group.

Johnatan Reiss contributed reporting.