"Afghan and Isaf forces repelled a number of insurgents when they attacked Jalalabad airfield this morning using a vehicle-borne improvised explosive device, rocket-propelled grenades, and small arms fire," it said in statement.
About 2,700 military and civilian personnel are based at the site in eastern Afghanistan.
The attack was similar to one on May 19 at the Bagram airfield north of Kabul and another three days later att Kandahar airfield in the south.
"The Taliban said they entered the airport," Zeina Khodr, Al Jazeera's correspondent reported from Kabul, the capital.
However, a spokesperson for Isaf told Al Jazeera that the Taliban did not breach the perimeter of the base.
"Isaf said it was a complex operation that involved a car bombing followed by an attack with small arms and rocket propelled grenades," Al Jazeera's Khodr said.
"Violence [in Afghanistan] is really at an all time high.
"June has been the deadliest month for international forces ... since the war began nine years ago."
The Taliban said the attack was a message to David Petraeus, the head of US Central Command who has been nominated to takeover leadership of Nato and US operations in the country, that they can strike at will, Khodr said.
Petraeus on Tuesday warned, during a US senate committee confirmation hearing, that there would be a "tough fight" ahead in Afghanistan.
Ahmadshah Aamadzai, a former Afghan prime minister, said the Taliban showed that "their intention is clear, they will struggle and fight ... until the foreigners leave Afghanistan".
Fahim Dashty, an Afghan political analyst, said that such an attack showed that there was little chance of reaching a political deal with the Taliban to end the violence.
"Political process can be successful only if both sides are willing to negotiate and to make peace," he said.
"But this is not the case in Afghanistan. One side is Taliban, which is terrorism, international terrorism; they are not willing to negotiate with us.
"They do not want to negotiate with neither the Afghan government nor the international community. How can you bring them to the negotiation table?"
Also on Wednesday, Eric Holder, the US attorney general, arrived in Afghanistan with a team of lawyers from the US justice department to discuss the fight against corruption with Afghan officials.
"Fighting corruption and supporting the rule of law in Afghanistan are top priorities for this administration, and we will continue to assist the Afghan government in creating and sustaining the effective criminal justice system to which the Afghan people are entitled," Holder said in a statement.
Holder's trip marks the first visit to Afghanistan by a US attorney general.