"We are in a global struggle against thugs and killers. And the United States of America has got to continue to take the lead."
Kabul parade assault
Bush's speech came after the Taliban attacked a military parade in Kabul attended by Hamid Karzai, the president.
At least six people, including a member of parliament and three attackers, were killed and nine others wounded in the assault near the presidential palace on Sunday.
The assault was an embarrassment for Afghan authorities, taking place at an event that was supposed to showcase the Afghan army's growing strength.
The Taliban said it had launched the attack to show it had the power to strike even the nation's biggest annual military parade.
More than 1,000 people have died in violence related to attacks by Taliban fighters and their supporters so far this year, according to an Associated Press count.
Despite the Kabul attack, in which six people were killed, Kai Eide, the UN envoy for Afghanistan, told Al Jazeera that Taliban raids were not spreading to government-controlled areas on a regular basis.
"I think you will see incidents outside that area, but generally that is not the case and we are, together with the Afghan army, making progress in combating security," he said.
Eide said it was important for the Afghan government to take control of security themselves.
The "most important thing we can do is invest in [the] Afghan army and police," he said.
Onus on Afghans
"Afghanistan is their country - we are very preoccupied in seeing to it that Afghans can take the lead themselves, not only on security side but across the board," Eide said.
"That has to remain our highest priority."
The training of the Afghan national army, numbering more than 64,000 soldiers, is scheduled to grow to 80,000 by the end of this year.
The US, frustrated by the reluctance of some European Nato allies to send troops to help out in fighting in southern Afghanistan, has sent 3,200 marines to support British, Canadian and Dutch forces there.
Of those 3,200 marines sent to Afghanistan, about 800 are involved in training Afghan security forces.