"Of course, our troops will respond to U.S. commanders," Mr. Bush said, with Karzai standing at his side at the White House. At the same time, Mr. Bush said the relationship between Washington and Kabul is "to cooperate and consult"
Mr. Bush also said that Afghan prisoners under U.S. control in Guantanamo Bay, Cuba, and elsewhere, would be slowly returned to their home countries.
"We will do this over time," he said. "We have to make sure the facilities are there."
Mr. Bush had high praise for Karzai as a valued anti-terror partner and credited the Afghan leader with "showing countries in the neighborhood what's possible."
But Karzai came to their meeting with a long list of grievances. Among them: more control over U.S. military operations, custody of Afghan prisoners held by the United States and more assistance in fighting opium trade.
As for the opium trade, Mr. Bush said, "I made it very clear to the president that we have got to work together to eradicate the poppy crop."
Karzai said that he hoped Afghanistan would be free of poppy crops within five to six years and that Afghan farmers could find alternative crops like honey dew melons and pomegranates.
There are about 20,000 U.S. troops in Afghanistan, costing about $1 billion a month. That is in addition to approximately 8,200 troops from NATO countries in Kabul and elsewhere.