U.S. National Security Adviser Gen. James Jones, prior to Obama's arrival Sunday, had briefed reporters on the visit, Obama's first since becoming president, saying its purpose was to inform Karzai about the need to improve performance by his corruption-riddled government, The Times of London reported.
At a news conference in Karzai's presidential palace, Obama, showing support for his counterpart, said: "The American people are encouraged by the progress that's been made."
Obama expressed hope of seeing improved governance, anti-corruption efforts and judicial process.
Karzai thanked the U.S. president for America's support, adding he hoped for the continuation of the partnership between the two countries. Karzai was invited to visit Washington, with a date set for May 12, the BBC report.
Addressing U.S. troops and civilians at Bagram Air base, Obama expressed confidence they would be victorious.
"There is no visit that I consider more important than this visit I am making now," said the president, who in December ordered an additional 30,000 U.S. troops to Afghanistan.
The Kabul visit capped a week of several pluses for Obama including the passage of health reform legislation, an arms control deal with Russia and his firm stance in talks with Israeli Prime Minister Binyamin Netanyahu, The Times of London said.