Zalmay Khalilzad's comments come as renewed fighting for days has plagued Afghanistan's southern Helmand province.
The car bombing struck near the entrance of the provincial police chief's office.
Multiple U.S. officials said Friday that the Pentagon has not received an order to cut troops to 2,500.
The Taliban pledge came after a meeting with U.S. peace envoy Zalmay Khalilzad and U.S. Gen. Austin Miller.
The two Soviet-era Mi-17 helicopters crashed due to technical problems while taking off in Nawa district, the ministry said.
The Joint Chiefs chairman said that U.S. troops will remain in Afghanistan well into next year.
The announcement of U.S. strikes comes after a gun battle on Monday was reported in and around Lashkar Gah.
U.S. President Donald Trump has vowed to bring American troops home by Christmas.
Taliban spokesman Zabihullah Mujahed said Trump's statement was welcome and he considered it a positive step.
"We should have the small remaining number of our BRAVE Men and Women serving in Afghanistan home by Christmas!" Trump wrote...
Seven new recruits will head to basic military training at Lackland Air Force Base, Texas.
The study next heads into a peer review before its findings can be submitted for a scientific journal.
The long-delayed project will tell the story of the American soldier through treasured artifacts.
AAVs rarely sink and fatal mishaps are uncommon for the 26-ton tracked vehicles.
It has been 15 years to the day since Cashe hauled his teammates out of the Bradley hit an IED near Daliaya, Iraq.