A Taliban spokesman claimed responsibility several hours after the attack, claiming fighters had acted "using exact information" about where the aircraft would be.
Rocket and mortar fire is not uncommon at the sprawling Bagram airbase and officers said they did not believe Gen Dempsey's plane had been directly targeted.
However the attack will have embarrassed coalition commanders and handed the Taliban a propaganda coup.
Gen Dempsey had held meetings with Afghan generals to discuss the growing threat of "green on blue" killings, where Afghan security personnel have turned their guns of their Nato allies.
The incident is not the first security scare to overshadow a visit to Afghanistan by a coalition leader.
David Cameron earlier this year had to order a review at Camp Bastion, Britain's main base in Helmand, after an Afghan worker evaded a security cordon in a stolen truck and made his way onto a runway as the US Defence Secretary was arriving.
The man then apparently set the 4x4 vehicle on fire before driving at high speed towards a party of officials waiting to greet Leon Panetta's plane.
In 2010 Mr Cameron had to change his schedule after intelligence officers said they believed the Taliban had identified his helicopter and were going to try and shoot it down.
Barack Obama made a brief overnight visit to Kabul earlier this year to proclaim a new dawn for Afghanistan after the allies had agreed a long term strategic pact. He arrived after nightfall and left before sunrise under heavy security precautions.
Rocket and mortar fire is not uncommon at the sprawling Bagram airbase and officers said they did not believe Gen Dempsey's plane had been directly targeted.
However the attack will have embarrassed coalition commanders and handed the Taliban a propaganda coup.
Gen Dempsey had held meetings with Afghan generals to discuss the growing threat of "green on blue" killings, where Afghan security personnel have turned their guns of their Nato allies.
The incident is not the first security scare to overshadow a visit to Afghanistan by a coalition leader.
David Cameron earlier this year had to order a review at Camp Bastion, Britain's main base in Helmand, after an Afghan worker evaded a security cordon in a stolen truck and made his way onto a runway as the US Defence Secretary was arriving.
The man then apparently set the 4x4 vehicle on fire before driving at high speed towards a party of officials waiting to greet Leon Panetta's plane.
In 2010 Mr Cameron had to change his schedule after intelligence officers said they believed the Taliban had identified his helicopter and were going to try and shoot it down.
Barack Obama made a brief overnight visit to Kabul earlier this year to proclaim a new dawn for Afghanistan after the allies had agreed a long term strategic pact. He arrived after nightfall and left before sunrise under heavy security precautions.