A heroic Army captain who charged into Taliban gunfire to save his buddies four years ago was finally awarded the Medal of Honor on Tuesday — and is seeking to re-enlist.

Former Capt. William Swenson, 34, became the sixth living recipient of the nation’s highest military honor for his role during the seven-hour Battle of Ganjgal in September 2009, one of the most brutal of the Afghan war.

President Obama recounted how Swenson dodged enemy fire, without a helmet, and risked his life to recover bodies and help save fellow troops.

“Will Swenson was there for his brothers,” Obama said at a White House ceremony. Swenson was visibly moved as the president described his heroics.

The president noted that a video, taken by cameras mounted on the helmets of evacuation helicopter pilots, showed Swenson delivering a severely wounded soldier, Sgt. 1st Class Kenneth Westbrook, to the helicopter.

The video showed Swenson bending down to kiss Westbrook’s forehead before running back into battle.

Westbrook, who succumbed to his wounds weeks later, was one of five Americans and 11 Afghans who died in the battle near the Pakistani border.

“In moments like this, Americans like Will remind us of what our country can be at its best, a nation of citizens who look out for one another, who meet our obligations to one another not just when it’s easy, but also when it’s hard — maybe especially when it’s hard,” Obama said.

After the battle, Swenson demanded to know why his repeated requests for air backup went unheeded. Following a lengthy investigation, two officers were severely reprimanded.

But the paperwork nominating Swenson for the Medal of Honor, which was submitted in December 2009, was lost, the Army said. The military is investigating charges that the honor was delayed because of Swenson’s complaints about lack of backup.

Swenson left the Army in February 2011 due to what he called “forced early retirement” and is unemployed and living in Seattle. Military sources said he has made the extraordinary request to return to active duty.