Mr Bush welcomed Mr Karzai, one of his key allies, at his Camp David retreat where they were expected to confer over the Taliban insurgency and mounting civilian casualties in Afghanistan.
VIDEO: Two day visit
The drug trade, economic development and the fate of 21 South Korean hostages held by the Taliban were also likely to be high on the agenda for the two days of discussions.
But Mr Karzai, who rose to power in 2002 with US backing, introduced a potential wrinkle in the talks with some friendly public comments about Iran, considered by Washington a major threat to global stability.
In an interview broadcast Sunday on CNN, Mr Karzai appeared to turn back US allegations that Iranian arms were helping to erode the security situation in Afghanistan.
“So far, Iran has been a helper and a solution," he says.
"Iran has been a supporter of Afghanistan, in the peace process that we have and the fight against terror, and the fight against narcotics in Afghanistan," Mr Karzai says.
He went on to say that Afghanistan and Iran had "very, very good, very, very close relations. … We will continue to have good relations with Iran.
“We will continue to resolve issues, if there are any, to arise."
Iran seen as ‘challenge’
His remarks differed markedly from the US stance, which sees Iran as a major menace that bankrolls terrorists, supplies arms to insurgents in Afghanistan and Iraq, and seeks to develop nuclear weapons.
The US position was reiterated Sunday by US Secretary of State Condoleezza Rice as she defended the US decision to sell tens of billions of dollars in arms to Saudi Arabia and other Gulf states to thwart Iranian ambitions.
"I don't think anybody doubts that Iran constitutes a major challenge, security challenge, to our friends, our allies, and therefore to our interests in the Gulf region," Ms Rice told CBS television.
The White House earlier said Mr Bush and Mr Karzai would discuss Washington's war on terror and "review their work together to enhance Afghanistan's long-term democracy, prosperity, and security."
The Taliban insurgency began months after their 2001 ouster by US forces and has intensified recently, having already claimed thousands of lives, mainly of militants.
Rising civilian deaths
But a counter-offensive by US and NATO forces has led to increasing civilian deaths, and Mr Karzai has angrily accused foreign soldiers of an "extreme use of force."
At least 600 Afghan civilians have been killed in insurgency-linked violence this year, half of them by international forces, according to statistics used by the United Nations.
Many of the deaths have been caused by the coalition tasked with hunting down Taliban militants and their Al-Qaeda allies believed to operate along the rugged Afghan-Pakistan border.
"We would like that situation to get much, much better," Mr Karzai said on CNN.
"We have to do everything that we can to reduce civilian casualties.
“They are allies in the fight against terror, and allies have to be protected."
Mr Bush is expected to reassure him that the US and NATO are concerned about the bloody repercussions and understand the political pressure he is facing.
The two leaders were expected to give particular attention to the Taliban's kidnapping of 21 South Korean aid workers, two of which have since been killed by their captors.
Mr Karzai told CNN that he would do everything to help free the South Koreans, "other than encouraging hostage-taking and terrorism to have them released."
He did not elaborate.
With Mr Karzai's government refusing demands to exchange Taliban prisoners for the South Koreans, Seoul is pressing the United States to intervene.
A top US diplomat said last week there was "potential" for military pressure against the Taliban to try to free them and end the biggest mass hostage-taking by the militants since the US-led invasion nearly six years ago.