The increased support includes six additional B-52 Long Range Strike bombers and 12 fighter bombers.
It comes after four B-52s were deployed to the region at the end of April to support the drawdown.
US Secretary of Defense Lloyd Austin has also extended the Eisenhower Carrier Strike Group.
"We're going to do everything that we can to make this drawdown deliberate, orderly and safe and to protect our people and our partners," Mr Austin said.
He added the Afghan forces are capable and said the US will "continue to support" Afghanistan.
"We will remain partners with the Afghan government, with the Afghan military; and, certainly, we hope through our continued support, the Afghan security forces can be effective," he said.
British troops are in Afghanistan in a training role as part of a NATO mission.
America is aiming to withdraw all of its forces from the country by 11 September - the 20th anniversary of the 9/11 terror attacks in the US.
Under the Trump administration, the US had agreed with the Taliban to withdraw all its troops from Afghanistan by 1 May 2021, but that was pushed back by President Joe Biden in April.
Army General Mark Milley, chairman of the US Joint Chiefs of Staff, said the US has been transferring responsibilities to Afghan forces "for [a] considerable amount of time".
He added: "To date, we have closed one base in Helmand; approximately 60 C-17 equivalents have departed with various equipment and rolling stock; and over 1,300 pieces of equipment, have been transferred either to the Defense Logistics Agency for destruction or to the ANSF for their use."
Gen Milley said the aim of the withdrawal mission is to conduct "a responsible co-ordinated and deliberate retrograde of US forces from Afghanistan, in good order".
The drawdown will be synchronised with allies and partners and, throughout the process, diplomatic efforts will continue between the Afghan government and the Taliban, the Pentagon said.
While there have been no attacks against US and partner forces, Gen Milley said "there continued to be sustained levels of violent attacks" from the Taliban against the Afghan National Security Forces.
"There have been about 80 to 120 enemy-initiated attacks a day for the past year," he said.