Peter Kuban [Vittorio Gassman] is a Hungarian displaced person and a survivor of World War II Nazi concentration camps. He stows away in Trieste on a ship bound for New York City. However, he is spotted by ship officials and held for American authorities. When the ship arrives in New York, he claims that he qualifies for entry under an exception for those who helped Allied soldiers during the war, but all he knows about the paratrooper he hid from the enemy is that his name is Tom, that he plays the clarinet in a jazz band in Times Square and that before they parted company in Europe, he gave him his military wristwatch which Peter now wears on his wrist. The immigration authorities, led by Inspector Bailey [Douglas Spencer], say that without better documentation he must be sent back to communist Hungary on the same ship, which departs the next morning.
Kuban escapes by leaping off the ship to the dock below, but breaks some ribs, then begins his search for Tom. Peter’s picture and a caption of him being wanted is plastered over the front page of the city’s tabloids, turning him into a wanted man and intensifying the urgency of his flight.
He encounters unemployed factory worker Maggie Summers [Gloria Grahame] in a crowded restaurant. When she steals a coat off a rack, Maggie is spotted and flees. Peter follows after her and helps her elude the police. They retreat to Maggie’s apartment, where she tends his injury as best she can. When her landlady, Mrs. Hinckley [Elizabeth Slifer], threatens eviction for being behind on her rent, Peter gives Maggie all the money he has. Eddie Hinckley, the landlady’s bullying son, barges in and sexually harasses Maggie. Peter bursts out of hiding and starts fighting him, but he is quickly overwhelmed. Maggie knocks Eddie out with a chair and flees with Peter, driven by a growing sense of solidarity and desperation.
The Hinckleys notify the police, claiming Peter was the attacker. He becomes a person of interest in an aggravated assault investigation, described as dangerous and possibly armed. Meanwhile, Tom [Jerry Paris] discovers Peter’s picture on a discarded newspaper and wants to rush to the immigration department, but his girlfriend Nancy [Ann Robinson] convinces him to attend an important audition instead. Tom impresses band leader Jack Teagarden [Jack Teagarden], but leaves abruptly to try to help Peter, balancing his dreams with the urgent need to aid a fellow traveler.
The fleeing couple try to hide out in the subway, but they are recognized. The police grab Maggie, but Peter manages to escape. While Maggie is questioned by authorities, she meets up with Tom. After hearing Tom’s account, Inspector Bailey begins to believe Peter’s story, but only if they can reach him before the ship departs at 7 am. If Peter is found after that deadline, he would be guilty of a felony for jumping ship, deported, and forever ineligible for admission to the United States.
The trio drives around in a tense scramble, searching for him. Suffering from his injuries, Peter slips into an unoccupied taxi and collapses. Burlesque dancer Tanya [Robin Raymond] gets involved after work and recognizes him from the newspaper photo. She takes him to her apartment to rest and eat. In a quiet moment, her disguise as Tanya gives way to her true identity as Bella Zakoyla, a fellow "Hunky." Her immigrant mother approves, but her criminal brother fears police getting involved, arguing that Peter’s predicament is the United Nations’ problem. He slips away, leaving a note apologizing to Tanya for causing trouble.
Acting on Freddie’s assertion, Peter heads toward the United Nations building early in the morning. He is spotted and the authorities close in on him. Maggie, Tom, Bailey, and two officers pursue Peter through the halls of the U.N. Unable to find anyone who will intervene on his behalf, he delivers a heartfelt soliloquy to an empty meeting room of the U.N. Human Rights Commission, addressing the imagined representatives of the world’s nations and insisting that peace and freedom depend on granting rights to every individual. As the chase tightens, Peter panics, climbs to the roof, and leaps toward the street—only to slip and fall backward onto the parapet. In a final turn, Maggie and Tom reach him, and the sound of Tom’s voice reaching Peter helps him find his footing. The pursuit ends with the three of them together on the roof, where they are finally reassured that Peter is safe and that their shared hope for a better future remains within reach.