MOSCOW -- A deal between the United States and Russia to increase assistance and training in Afghanistan is being hailed by Obama administration officials as "historic" and demonstrative of two nations no longer fighting a Cold War.

A joint statement issued Monday before a press conference in Moscow with President Obama and Russian President Dmitri Medvedev pledges a commitment to the nation of Afghanistan as it struggles to overcome various political and social challenges.

"We reaffirm our commitment to the goals of the common fight against the threats of terrorism, armed extremism, and illegal drug trafficking in Afghanistan," the statement reads. "We shall continue and develop our cooperation in the interest of enhancing the capabilities of the government of Afghanistan to accomplish key socioeconomic objectives, to raise living standards, and to ensure the security of its people."

The statement was a bit lost in the news in a series of agreements, including on the Strategic Arms Reduction Treaty, and senior administration officials chided reporters for focusing on a Cold War type of relationship between the two nations. 

"This is not the Cold War. This is not just a relationship about competition, confrontation and the things we disagree about," said Michael McFaul, a senior adviser on Russia. "This discussion makes me feel a little bit like some of us want to fight what is not a real war. It is not real. The threat that we pose to Russia from our missile defense systems is not real. The president couldn't have been more clear about that."

McFaul highlighted the Russians allowing 4,500 flights of American soldiers and equipment going through Russia, a country he admitted, used to be an adversary. "We're talking about 4,500 flights of American soldiers and equipment going through what used to be our enemy. And they're paying for it. This is something that's very concrete. This is a real war we're fighting."

The United States' rough calculation is that the flights will save around $133 millions in navigation fees, a cost the Russians will now pick up.

One irony that went unmentioned in the announcement was the U.S. role in helping defeat Russia in Afghanistan in the 1980s in what was seen as one of the last Cold War stands before communism fell in the Soviet Union.

The White House wanted to highlight progress on various efforts the two presidents reached Monday, saying there was more than one or two signing statements about missile defense and START. 

"The eight or nine things that we did agree upon and the multi-dimensional relationship that we're trying to put together in a very short period of time is what we really talked about, not this part where we have so much contention," McFaul said.

FOX News' Eve Zibel contributed to this report.