Two U.S. veterans who volunteered to fight in Ukraine have gone missing, their families said on Wednesday.

One man was named Alex Drueke, 39, a former U.S. Army staff sergeant who served two tours in Iraq, his family said in a statement. The other was named Andy Tai Ngoc Huynh, 27, a former Marine, Darla Black, the mother of Mr. Huynh’s fiancée, Joy Black, said in a phone interview.

The U.S. State Department said on Wednesday that it was “aware of unconfirmed reports of two U.S. citizens captured in Ukraine.”

“We are closely monitoring the situation and are in contact with Ukrainian authorities,” a State Department spokesperson said. “Due to privacy considerations, we have no further comment.”

Mr. Drueke and Mr. Huynh disappeared together when their platoon came under “heavy fire” on June 9, leading all its members to fall back except for the two of them, according to a statement sent by Mr. Drueke’s family. Reconnaissance by foot and drone did not turn up any sign of the two soldiers, the statement continued.

“This could mean they are in hiding or it could mean they have been captured,” said Mr. Drueke’s mother, Bunny Drueke. She added in an email that “intercepted communications” indicated the two Americans might have been captured, but that had not been confirmed.

The two men, if captured, would be the first Americans known to have become prisoners of war during the conflict.

The Drueke family was notified of the search for the two missing Americans by another member of the platoon on Monday, the family’s statement said.

“When Russia invaded Ukraine, Alex immediately told me he wanted to go use his skills to train Ukrainians in how to operate American weaponry,” said Mrs. Drueke. “He isn’t married, he doesn’t have kids, and he has the training and the experience. He felt it was his duty to help defend democracy, wherever needed.”

The statement described Mr. Drueke as an avid hiker who before the war had been living on family land in rural western Alabama while hoping to plan “a new adventure” with his Mastiff rescue, Diesel.

In an interview with WAAY-TV, an ABC affiliate in northern Alabama, Mr. Huynh, who was identified as living in a small city in the region, Hartselle, and being from Orange County, Calif., said that he had decided to travel to Ukraine and fight after seeing 18-year-olds fighting for their freedom.

“I know there’s a potential of me dying,” he said. “I’m willing to give my life for what I believe is right.”

Before going to Ukraine, Mr. Huynh studied robotics at a local college that Joy also attended, Ms. Black said. He had been in the Marines for four years, entering right after graduating from high school.

“Andy didn’t make the easy choice, he made the right choice,” Joy said through sobs in a phone interview. “Andy did not go there for an adventure. He just wanted to help.”

Both the Black and Drueke families said they had last heard from the men on June 8, when each said they would be out of reach for a few days.

“Alex’s family has become our family,” Ms. Black said. “If there is anyone who understands how my daughter feels right now, it’s Alex’s mother, so we all feel connected.”

An Alabama congressional delegation — including Senators Richard Shelby and Tommy Tuberville, as well as Representatives Terri Sewell and Robert Aderholt, who represent the men’s districts — is coordinating with the State Department, said Ms. Sewell’s chief of staff, Hilary Beard. A spokesperson for Gov. Kay Ivey added that the delegation was also working with the F.B.I.

Since the war began on Feb. 24, an unknown number of foreigners have volunteered to help Ukraine in various ways, among them hundreds of American military veterans who have sought to join combat. The State Department reiterated in its statement that U.S. citizens should not travel to Ukraine.

There have been no confirmed reports of Americans being captured, and only one American has been reported dead: Willy Joseph Cancel Jr., 22, a former Marine infantryman from Kentucky who was killed on April 24 or 25 when his unit was overrun by Russian troops, Mr. Cancel’s uncle, Christopher Cancel, said in an interview with The New York Times.

Western governments and human rights groups were rattled last week when a court in Russia-occupied eastern Ukraine sentenced two Britons and a Moroccan man to death, accusing them of being mercenaries.

Dave Philipps contributed reporting.