Lebanon’s caretaker prime minister, Najib Mikati, appealed to the United Nations on Friday to adopt a resolution calling for an “immediate” cease-fire between Israel and Hezbollah, the latest attempt by his embattled government to bring an end to the violence in Lebanon that has killed thousands and displaced nearly one million.

“The diplomatic solution remains on the table,” Mr. Mikati said in a televised address, in which he urged the parties to return to the provisions of a 2006 U.N. agreement on demilitarizing the countries’ shared border, adopted after the previous war between Israel and Hezbollah.

The measure, Security Council Resolution 1701, has been largely ineffective. Hezbollah, an Iran-backed militant and political group, still exercises de facto control over southern Lebanon, the area along the border with Israel, and has not laid down its arms. In fact, the group has entrenched itself militarily in the region since the 2006 war, amassing a vast stockpile of weapons and missiles along the border.

Israel, similarly, has not upheld its side of the bargain and has been accused by the United Nations and Lebanon of violating Lebanon’s territorial sovereignty.

Pushing the U.N. to call for a cease-fire, Mr. Mikati said on Friday that Lebanon wanted to see “the deployment of the army in the south and the bolstering of its presence along the border.”

Despite the military’s being one of the few institutions in Lebanon that holds cross-sectarian support, it is largely reliant on U.S. funding and considered by many as incapable of defending against Israel. Lebanon’s crisis-racked caretaker government is also largely powerless to rein in Hezbollah.

“Hezbollah,” Mr. Mikati added, “is in agreement on this issue.” But at a news conference on Friday, a Hezbollah spokesman indicated that the group had no plans to wind down its fighting with Israel soon.

“The battle with the Zionist enemy is still in its earliest stages,” said Mohammad Afif, the head of Hezbollah’s media office.