The four American soldiers were pinned down in June 1968, taking intense fire from the enemy near the hamlet of Ap Go Cong in Vietnam. The large Huey helicopter sent to rescue them had abandoned its attempt, citing the great likelihood of failure.

But First Lt. Larry L. Taylor refused to give up.

Flying in his two-man Cobra helicopter, which was nearly out of ammunition, Mr. Taylor landed in the middle of the firefight, extracting the four men who hung onto the helicopter’s skids and rocket pods as the helicopter carried them to safety. It was the first time a rescue like that had even been attempted during the war.

On Tuesday, President Biden awarded Mr. Taylor the Medal of Honor at the White House, citing his “conspicuous gallantry” for rescuing the soldiers “under heavy enemy fire and with complete disregard for his personal safety” more than five decades ago.

“That’s valor. That’s valor,” Mr. Biden said before draping the medal around Mr. Taylor’s neck in the East Room. “That’s our nation at its very best.”

Mr. Biden arrived for the ceremony wearing a mask because the first lady, Jill Biden, tested positive for the coronavirus on Monday evening. Mr. Biden has tested negative twice since then, but White House officials said he planned to wear a mask when he was indoors and around other people.

Still, the president removed his mask when he began speaking, with Mr. Taylor sitting on a chair about 15 feet away.

“All of us today are inspired by the story, and they will be, of how, of how he refused to give up, refused to leave a fellow American behind, refused to put his own life above the lives of others in need,” the president said.

After Mr. Biden finished putting the medal around Mr. Taylor’s neck, the two men shook hands and saluted each other. Mr. Biden quickly left the room, departing even as the benediction was being read.

Mr. Taylor joined the Army on June 5, 1966, eventually rising to the rank of captain before being honorably released from active duty in the summer of 1970.

For his actions on that day in 1968, Mr. Taylor was awarded the Silver Star. On Tuesday, Mr. Biden upgraded the award to the Medal of Honor, setting the stage for the White House ceremony.

According to Mr. Biden, Mr. Taylor was providing support for a long-range reconnaissance patrol in Vietnam on the afternoon of June 18, 1968. The four-man team of soldiers on the ground was surrounded by as many as 100 enemy fighters, who were closing in on their position.

Mr. Taylor’s helicopter was not intended to be used for rescue missions, Mr. Biden said in describing the fighting that took place on an eerily dark night. And after 45 minutes of attack runs in an effort to save the soldiers on the ground, Mr. Taylor was running out of fuel and was almost out of ammunition. Despite that, he used the landing lights on his helicopter to distract the enemy forces so the soldiers could reach an extraction point he had designated.

Mr. Biden said Mr. Taylor’s helicopter was repeatedly hit with fire from the ground, and had only a few minutes’ worth of fuel left when he made the final attempt to retrieve the soldiers.

“When the team reached the site, Taylor landed his Cobra under heavy enemy fire and with complete disregard for his personal safety,” the White House said in a news release.

Once the patrol team climbed aboard, Mr. Taylor flew to safety.

The president said that the men quickly jumped off the helicopter after it landed in safe territory, and that Mr. Taylor did not see some of them for 30 years. Mr. Biden said that in recent years, family members of those men have approached Mr. Taylor.

“You don’t know me, but you saved my daddy’s life,” Mr. Biden said they told him.

The Medal of Honor is awarded to members of the military who “distinguish themselves conspicuously by gallantry and intrepidity at the risk of their own lives above and beyond the call of duty,” the White House said.

The conduct must involve bravery or self-sacrifice to a degree that distinguishes a person from colleagues on the battlefield. And there must be “incontestable proof” of the conduct in question.