"This deadly attack was carried out by a valorous Afghan army member when the officials [Americans] were busy gaining information about the mujahideen," Zabiullah Mujahid, a Taliban spokesman, said in an email.
The Afghan defence ministry denied that an Afghan army officer was involved in the attack and said none were stationed at the base.
"This is the Taliban talking and nothing the Taliban says should be believed," Zahir Azimi, a ministry spokesman, said on Friday.
But a spokesman for Nato-led forces in Afghanistan acknowledged that Afghan security forces were working on the base.
Julie Reside, a US state department spokeswoman, said plans to increase the US civilian presence in Afghanistan remained on track and that security would continue to be a primary concern.
The CIA did not release the names of those killed or provide details about the work they were doing, citing "the sensitivity of their mission and other ongoing operations".
In a letter to CIA employees, Barack Obama, the US president, wrote: "Your triumphs and even your names may be unknown to your fellow Americans, but your service is deeply appreciated."
He announced that stars would be added in the names of the fallen agents to the 90 already on the Memorial Wall at CIA headquarters honouring agents who have fallen in the line of duty.
US officials said an Afghan was also killed in the attack and six CIA employees were wounded.
The chief of the CIA's operation at the Forward Operating Base Chapman was among the seven dead, according to a former intelligence official.
Al Jazeera's Hashem Ahelbarra, reporting from the Afghan capital, Kabul, said on Friday the CIA had outposts near the Pakistani border for launching drone attacks against the Afghan Taliban, al-Qaeda and the Pakistani offshoot of the Taliban.
"Two days ago the roles were reversed and the prey suddenly decided to hunt down the CIA deep into their base.
"What we don't know exactly is how this [attacker] was summoned into the base, whether he was checked or not."
The US has committed to send hundreds of civilians to support work on development projects that aim to undermine support for the Taliban and other fighters.
But as the security situation in Afghanistan has deteriorated, many of the civilians working outside Kabul have retreated to army bases.
In a separate attack on Wednesday, five Canadians were killed in the southern province of Kandahar.
The group, made up of four soldiers and a journalist accompanying them, were visiting community reconstruction projects and were killed when their armoured vehicle was hit by a bomb, the Canadian defence ministry said.
The journalist, Michelle Lang, worked for The Calgary Herald.
The Calgary Herald said Lang had been in the country since December 11 and was the first Canadian journalist to die in Afghanistan since Ottawa joined the international mission there in 2002.