(L to R) Ron Rifkin as Menachem Begin, Richard Thomas as Jimmy Carter and Khaled Nabawy as Anwar Sadat in Camp David at Arena Stage at the Mead Center for American Theater March 21-May 4, 2014. (Teresa Wood/Teresa Wood)

In one of the best scenes of “Camp David,” the alternately talky and affecting new play at Arena Stage about the 13 grueling days of negotiations that led to the Middle East’s most durable peace treaty, President Jimmy Carter takes Egypt’s Anwar Sadat and Israel’s Menachem Begin on a class trip of sorts to Gettysburg, Pa.

At the site of one of America’s bloodiest battles — and Abraham Lincoln’s greatest speeches — the three leaders at last can focus on something other than their rote, self-serving agendas. It’s on this field of grief and carnage that these men who’ve known war become reflective about suffering and what they’ve learned from it. And as Begin starts to speak the words of the Gettysburg Address, and Carter joins in, and then Sadat, you can be excused for choking up at the kumbaya affirmativeness of the interlude — the emotion released at watching these figures grope their way to common ground.

Lawrence Wright’s play, receiving its world premiere at Arena’s Kreeger Theater under Molly Smith’s direction, is engrossing at these moments, because it’s not just reciting history or framing the debate; it’s also showing us how to understand why intractable adversaries might have lowered their guards, gazed at their bitterest enemy and begun to conceive of a way forward.

It’s also the sort of illuminating scene the play needs more of. Because when “Camp David” is chronicling the agonizing, two-steps-forward-one-step-back pace of geopolitical dealmaking, the drama tends to mirror actual events too authentically. It becomes a slog. And in its meticulous effort to reveal the singular achievement of those 13 days, it aspires to be more than that.

The characters with all the speaking roles in “Camp David” are the major players in the events of September 1978, when an American president went to the extraordinary length of sequestering himself with two intransigent leaders in the mountains of Maryland, with the intention of working out the details of peace, man to man to man. The actors form an impressive roll call: Richard Thomas is Carter, Ron Rifkin plays Begin, Egyptian film star Khaled Nabawy portrays Sadat and Hallie Foote is Carter’s first lady, Rosalynn.

Lawrence Wright’s ‘Camp David’ is at Arena Stage through May 4. Starring Richard Thomas, Hallie Foote, Ron Rifkin and Khaled Nabawy. Directed by Molly Smith. (Winyan Soo Hoo/The Washington Post)

Wright, a widely traveled, Pulitzer Prize-winning journalist, has created for them identities that are limited in the personality department. You sense the actors’ struggle — especially in the cases of Thomas and Foote — to project something more complex about these world-class newsmakers than the one admirable attribute propelling the evening, namely their desire to bring tranquil security to the Holy Land. Perhaps some of the apparent tightness onstage had to do with the fact that on this night, the audience included the Carters, along with a slew of other well-known Washington faces, onetime Carter aides and current members of Congress and TV journalists. It can’t be relaxing, practicing that Jimmy Carter high-beam smile for Jimmy Carter. In any event, this worthwhile play cries out for some shift in its priorities. It needs to become a bit more about the people and less about the process.

You crave more, too, for Rifkin and Nabawy to chew on, for Wright to loosen his strong journalistic grip on the material, to give us more of the dramatist’s poetic view and less evidence of the astute researcher. Both actors are very good at embodying the wiliness and steel of politicians callused by suspicion and the anxiety that blinking first might hold dire consequences, but also the worry that failing to seize the moment might be just as dangerous. Smith seems content here to rely on the actors’ considerable charisma to carry the story, and that works, up to a point. Rifkin expertly calls up Begin’s stoic resolve, while Nabawy impressively summons Sadat’s canny bonhomie. Even in these private talks, however, we see little of anything but the public men. (Giving them no confidantes other than the Carters — both had entourages at Camp David — proves theatrically constricting.)

The images of these leaders, engaged in a civil battle of wills amid the trees and cabins of Walt Spangler’s rustic set, reinforce one of the more hopeful takeaways from the play: that government can be a mechanism for good. In its references to Palestinian autonomy, Jewish settlements in lands Israel conquered in the 1967 war and Israel’s quest to dwell within safe borders, the play reminds us that the world still lives with issues left unresolved at Camp David. But unlike, say, the relentlessly negative view of Washington spread by the hit Netflix series “House of Cards,” this play suggests that it’s possible in American politics to want to do something other than help oneself.

The play’s biggest problem is turning that impulse into a consistently lively 100 minutes or so of exposition. The progress of these delicate negotiations would, of course, have to be frustratingly stop and start. Still, the scenes in which Begin and Sadat are seated in patio chairs, asserting and reasserting their countries’ grievan­ces and demands, while the referee president coaxes and cajoles, become a little monotonous. It’s not only the combatants who are relieved when Foote’s Rosalynn materializes amusingly from her cabin at just the right moment with a tea service and encouraging words.

Rosalynn makes so clear she doesn’t want to intrude that we become aware of a slyly opposite intent: Her genteel attentions are part of the diplomatic ballet. If anything, more of Rosalynn is needed in the play, and not just as sympathetic ear for her idealistic, spiritual husband, who addresses God directly, asking for guidance, much in the way Tevye pleads with his maker in “Fiddler on the Roof.” It’s a device that reinforces an antique dimension to the storytelling. And it isn’t balanced nearly enough with a sense of what resources (beside religion) Carter called on to compel Begin and Sadat to remain open to a breakthrough.

As detailed here, the president’s final desperate assault on Begin’s conscience to win an agreement — if a consciously manipulative act is what it was — comes across as so ambiguous that it registers more as a sentimental gesture than a stroke of genius. Historically accurate the depiction may be, but like too many other instances in “Camp David,” it misses an opportunity to exploit dramatic potential to the fullest.

Camp David

By Lawrence Wright, directed by Molly Smith. Set, Walt Spangler; costumes, Paul Tazewell; lighting, Pat Collins; original music and sound, David Van Tieghem; projections, Jeff Sugg; wigs, Chuck LaPointe. With Will Beckstrom and Will Hayes. About 1 hour 45 minutes. $55-$100. www.arenastage.org . 202-488-3300.