David Jackson

USA TODAY

President Obama paid tribute Thursday to Major General Harold Greene, who was killed Tuesday during an attack in Afghanistan.

Serving in Afghanistan "continues to be a difficult and dangerous mission," Obama said before signing a bill on veterans health care.

"Our prayers are with the Greene family, as they are with all the Gold Star families and those who have sacrificed so much for our nation," Obama said.

During his veterans' health care speech, the president also said:

"Four months from now, our combat mission in Afghanistan will be complete. Our longest war will come to an honorable end.

"In the years to come, many from this generation will step out of uniform, and their legacy will be secure. But whether or not this country properly repays their heroism, properly repays their patriotism, their service and their sacrifice, that's in our hands."