The organizers of the Middle East gathering at Annapolis, Md., should have screened “The Band’s Visit,” a gem of an Israeli movie playing in theaters in New York, instead of the grim replay of old footage we saw last month.

Of course, it is only a movie, and a very funny one at that, dealing with the so-called cultural exchanges that have taken place for decades under what we all know as a “Cold Peace.” Yet the film takes note of what many Arabs, Israelis, and most of the world does not realize: There is life, albeit in the slow lane, in the Egyptian-Israeli peace agreement of 1979.

Crisply executed, beautifully acted, charming, and brittle, “The Band’s Visit” is about an eight-man uniformed Egyptian police orchestra that lands in an Israeli desert town, where the locals greet the band members first with total indifference, then with growing warmth. Think of it as one of the funnier Coen brothers movies, just set in a Middle Eastern desert outpost instead of a quirky American town.

From the opening shot, it is clear that the Egyptians, natives of the teeming metropolis of Alexandria, are baffled by their predicament. But they quickly adapt to the contours of this weird desert hamlet, which is completely cut off from the big cities of Israel.

Taking steps toward camaraderie, if not friendship, the Egyptians and Israelis quickly discover a number of absurd commonalities, starting with the cutting sense of humor they share.

Amid the cacophony of this region’s constant conflicts, “The Band’s Visit” deftly explores the slivers of peace that have thrived in culture, commerce, and tourism since the Egyptian-Israeli pact of 1979.

Far from sweet, the movie is no sentimental celebration of this peace but an exposé of the many loony ways in which it has been settled. For their part, the Egyptians have matched this Israeli humorous examination with movies such as “The Embassy Is in the Building.”

That 2005 film is Amr Arafa’s hilarious take on the elegant building on the Nile in Cairo that housed the Israeli Embassy for some 30 years, transforming the structure’s social geography and the wild lifestyle of one tenant who could not have cared less about politics until his womanizing became a threat.

In the Israeli movie, the unsmiling leader of the Egyptian orchestra, Tewfiq — delightfully portrayed by Sasson Gabai — also speaks for the silent majority of Egyptians when he tells his band, after the initial shock of not being received by anyone at the airport in Tel Aviv and getting lost in the middle of nowhere, that they are still ambassadors of Egypt, even if they have not had a meal in two days and have no money and no place to sleep. Then he proceeds to deal with a town in which his orchestra elicits blank looks and a total lack of interest by arguing that they are artists first.

Similarly, Mr. Arafa’s “Embassy Is in the Building” contains no fire or brimstone about peace and war but revolves instead around the farcical situation of a playboy who suddenly finds his life under the scrutiny of Egyptian security and the Israeli ambassador, who is his next-door neighbor.

In both movies, peace boils down to people doing their best under the circumstances to find common denominators. Israelis and Egyptians are victims as well as heroes. In “The Band’s Visit,” as a critic for the New York Times noted, “Love doesn’t exactly bloom in this desert, but a sense of unarticulated longing does.” Ditto for the film’s Egyptian counterpart.

The Egyptian movie was a huge hit in the Arab world, where it remains a classic. The Israeli film has yet to be released there. It was banned at the Abu Dhabi film festival, held in mid-October. Egyptian censors may follow suit at Cairo’s upcoming film festival. We shall see if the Arab world ever gets to watch it.

The international distributor of “The Band’s Visit,” Sony Pictures Classics, is pushing it for consideration in some of the general Oscar categories, including best screenwriter and director. Even if it doesn’t score, I hope those in the Arab world who want to see it — a majority, in my view — get to triumph over the glum, boring militants who are trying to kill it.

ymibrahim@gmail.com