Georgian soldiers Sgt. Guram Beroshvili, left, 29, and Sgt. Alex Ormotsadze, 28, guard an entry point to an American base in southern Afghanistan in June. (Ernesto Londoño/The Washington Post)

When the United States pulled together international coalitions to support its wars in Iraq and Afghanistan, few allies volunteered as quickly and enthusiastically as this small former Soviet state.

As the Afghan war comes to a close after 13 years, the makeup of the multinational force has grown as anemic as the conflict has become unpopular. Yet Georgia, driven by an incessant quest to join NATO, is among the stragglers sticking it out until the end — and playing and outsize role.

The coalition of the willing, born during a moment when the fear of terrorist attacks gripped Western capitals, has become to a large extent a coalition of aspirants. For several small, militarily weak nations, the past decade of war has offered transformational opportunities by boosting their fighting prowess, providing access to world leaders and altering regional politics.

Georgia, which had 20 percent of its territory occupied by Russia in 2008, was among those motivated by a calculation that years of serving in combat zones alongside U.S. troops would earn it a spot in the alliance that binds members to come to each other’s defense.

While some troop contributors to the Afghan war have been welcomed to NATO or put on track to join the alliance, Georgia remains locked out — a source of particular consternation here at a time when Russia has just annexed part of Ukraine and continues to destabilize eastern Ukraine, according to alliance officials. Georgian officials are also upset that Washington has not processed requests for military equipment they want to buy in an effort to be better prepared should Georgia go to war with Russia again.

“Clearly, there’s a sense of disappointment in general that we’ve performed and contributed more than some NATO members,” Georgian Defense Minister Irakli Alasania said in a recent interview. “We don’t have any security guarantees, no security blankets. The only force we can count on is ourselves.”

Georgia’s 805-strong force in Afghanistan is roughly equal to the collective contributions of NATO members Spain (247), France (177), Denmark (165), Belgium (147), Portugal (66) and Greece (10). The only country that has more troops per capita is the minuscule and impoverished Pacific island of Tonga, which keeps some 55 soldiers in Afghanistan.

Unlike most other contingents in the Afghan coalition, Georgia has not demanded caveats to shield its soldiers from the riskiest assignments or spare them from fighting. It has made only two requests: to be trained by U.S. Marines and to be given chief responsibility for sectors of the Afghan battle space.

“They’ve distinguished themselves in terms of their valor,” said Evelyn N. Farkas, a deputy assistant secretary of defense whose regional portfolio includes Georgia. “They have suffered the way we have in terms of casualties.”

Georgian officials might sound bitter when speaking about the elusive NATO membership, which they blame primarily on opposition from Germany and France, strong commercial partners of Moscow. But they are not altogether ungrateful. The Afghan war provided the nation of 4.5 million with an opportunity to turn a ragtag, demoralized and poorly led military into a professional and increasingly capable fighting force.

With support and guidance from the U.S. military, Georgia recently built a state-of-the-art military academy with a culture and curriculum modeled after the vaunted U.S. Army school in West Point, N.Y. U.S. Marines run a training program on the outskirts of Tbilisi, the capital, for Georgian battalions preparing to deploy to Afghanistan.

On a recent afternoon, Capt. Christopher Machi, a Marine working with a Georgian battalion in southern Afghanistan, marveled at how far his trainees have come.

“Their small-tactics abilities are quite good,” he said. “They’re definitely a warrior culture, and they’ve been in heavy combat here during the last few years.”

Georgian soldiers deployed to Afghanistan are far from circumspect when discussing their role in backing their country’s political aspirations. Speaking at a base in Zabul province, where his unit was tasked with providing security for an American infantry battalion, 1st Lt. Gocha Giorgadze said he and his comrades understand what their sacrifice is about.

“During the war with Russia we saw a series of weaknesses in our army, and we have sought to improve those problems,” Giorgadze said, referring to the 2008 conflict during which Russian forces quickly overwhelmed the Georgian military. “Practice has shown us that everything is possible.”

Realizing that the prospect of NATO membership remains distant, Alasania, the defense minister, has been pressing Washington for help in boosting his country’s air defense systems and anti-armor capabilities. Like many Georgians, he speaks about a new conflict with Russia as a near-certainty.

“We’re now putting together capabilities that would cost Russia heavy losses” should a new confrontation materialize, Alasania said. “We don’t expect anyone to come fight our fight. What we’re looking for from the U.S. is to give us the tools to defend our freedom if it came to that.”

Some former U.S. officials who have observed the evolution of the Georgian military over the past decade say the Georgians are owed more than Washington has been willing to give.

“When we were in a corner, so many countries were willing to go with us,” said Damon Wilson, who oversaw European policy at the White House during the final years of the George W. Bush administration and is now executive vice president at the Atlantic Council. “We would be incredibly shortsighted to wash our hands of them.”

Retired Adm. James G. Stavridis, who stepped down as the top military commander of NATO last year, agreed. He said Georgia has earned a formal pathway toward joining the alliance, a process called a “membership action plan.” But he conceded that the misgivings of some alliance members are a significant impediment.

“There are reservations over the fact that 20 percent of their territory is occupied by a large and aggressive neighbor,” said Stavridis, the dean of the Fletcher School at Tufts University. “It would lead the alliance to a place where we would have to make some very difficult decisions.”

NATO officials have signaled that they will not give Georgia a formal accession plan during next month’s summit in Wales, although they expect to offer enhanced status as a partner nation of the alliance.

Stavridis said that the West’s quickly souring relationship with Russia, which began with Moscow’s annexation of Ukraine’s Crimea region earlier this year, could ultimately work in Georgia’s favor.

“As relations between NATO and Russia crater, it enhances the possibility over time of Georgia getting more equipment and training,” he said. And, if the current trajectory holds, perhaps Washington could persuade allies to put the country on a membership track.

“It would show the Russians that Russia doesn’t get a vote on who gets into NATO,” he said.