David Straitharn portrays Jan Karski in “My Report to the World: The Story of Jan Karski.” (Clinton Brandhagen)

David Strathairn can’t get the Georgetown professor out of his system.

It is a purely professional attraction, however, one that over the past year has propelled the Oscar-nominated actor back again and again to the story of the Polish-born academic with the haunting wartime past.

He first wore the guise of the late Jan Karski — declared one of the Righteous Among The Nations at Israel’s Yad Vashem Holocaust memorial — in a staged reading on the Georgetown campus. Then came an invitation from Warsaw to play Karski there, which was followed by an offer from American producers to refine the performance further. And that has led to the current embryonic workshop run of “My Report to the World: The Story of Jan Karski,” which makes a free-admission stop Monday night in Washington at Sidney Harman Hall.

What started as a once-only tribute to Karski, who taught at Georgetown for 40 years as a professor of government, has evolved into something deeper and more ambitious, with a final trajectory that is still unclear. An organization has been created, the Karski Theater Project, supported by a 40-member producer’s circle, to finance the development of the eight-actor play by Derek Goldman, artistic director of Georgetown’s Davis Performing Arts Center, and Clark Young, one of Goldman’s former students.

At the core of the project remains the 66-year-old Strathairn, who’s made a specialty of portraying cerebral, brooding men of recent history, such as Edward R. Murrow (“Good Night and Good Luck,” for which he was Oscar-nominated) and J. Robert Oppenheimer (in a PBS series). Karski was so traumatized by his experiences as a courier for the Polish underground, taking his reports on the Nazi genocide of the Jews all the way to the office of President Franklin D. Roosevelt, that he could not bring himself to speak of the events again for decades. It is his reckoning with the past that forms the central theme of “My Report to the World.”

“What’s really fascinating is discovering the roots of his psyche,” says Strathairn, during a lunch break this week from rehearsals in New York; the piece runs at the Museum of Jewish Heritage in Lower Manhattan — with the short detour to Washington — until July 25. “What compelled a man to do that: Why was he silent? And how he reconciled himself with the celebrity of it.”

Goldman, who directs “My Report to the World,” envisioned the piece as a facet of a program at Georgetown, the Laboratory for Global Performance and Politics, that finds intersections between theater and geopolitics. (Another of the Lab’s initiatives, hosting the American premiere last fall of “Syria: The Trojan Women,” was scuttled after the State Department refused to grant visas to the Syrian refugees cast in Euripides’s tragedy.) So the Karski play has roots in the dramatic and the academic. Audiences’ positive responses have motivated Goldman, Clark and their creative team to look for ways to make it more elementally stageworthy.

“At each step, we’ve been encouraged,” the director says. “The people who do know Karski have felt from the beginning that there’s something in the spirit of Karski that is being conjured.” They’ve frequently commented, he adds, on how uncannily Strathairn manages to evoke the professor, whose presence is immortalized on the Georgetown campus in a sculpture of him seated pensively on a bench.

As the 90-minute “My Report to the World” recounts, Karski was in his 20s when Hitler invaded Poland and he as a result enlisted in the Polish army. Later, he would join the Polish underground and be captured by the Nazis, who tortured him. After an escape, he began a stint as a messenger, shuttling between Nazi-occupied territory — where he witnessed the degradations of the Warsaw Ghetto and the horrors of a concentration camp — and the Polish government-in-exile in London. The play’s dramatic highlight is an account of his mission to Washington to apprise FDR and Felix Frankfurter, a Jewish justice on the U.S. Supreme Court, of the monumental scale of the atrocities. He’s met with skepticism and vague promises of help, which for the Jews of Poland never came.

Goldman observes that these days, because “there’s a fatigue with the notion of what is a Holocaust play,” he and the creative team have looked to freshen the approach. One way has been to recruit a choreographer, Emma Jaster, to provide interludes of movement, modeled on the work of Karski’s wife, dancer-choreographer Pola Nirenska, a Holocaust survivor who took her own life in 1992. (Karski died in Washington eight years later, at 86.)

Where “My Report to the World” might settle for a longer run is still being debated. Debbie Bisno, a New York producer who helped arrange the free workshop run at the Museum of Jewish Heritage, thinks there are natural connections for museums, educational institutions and regional theaters. (The U.S. Holocaust Memorial Museum is a partner, for instance, in the presentation at Harman Hall.)

For Strathairn, the opportunity to try to unlock the mysteries of a man who for so long kept quiet about his extraordinary life is a challenge worth returning to. “I’m formulating a theory, a personal theory,” the actor says about Karski’s reticence. “And it’s as valid as any other theory.”

My Report to the World: The Story of Jan Karski, by Derek Goldman and Clark Young. Monday at 7:30 p.m. at Sidney Harman Hall, 610 F St. NW. Admission free. To reserve tickets, visit shakespearetheatre.org.