The pair last met in May, when Obama visited Kabul to sign a strategic partnership agreement detailing relations between the two countries after U.S. forces depart. Under that agreement, the United States plans to hand over security responsibilities to the Afghan military by the end of 2014.

At that meeting, the president hailed "an enduring partnership" between the two nations.

"The agreement we signed today sends a clear message to the Afghan people: As you stand up, you will not stand alone," Obama said. "It establishes the basis of our cooperation over the next decade, including shared commitments to combat terrorism and strengthen democratic institutions. It supports Afghan efforts to advance development and dignity for their people."

The administration, though, is also considering plans that could maintain a sizable military presence in Afghanistan beyond that drawdown deadline.

According to CNN, Karzai also plans to meet with Secretary of Defense Leon Panetta during his trip to the United States. On Monday, President Obama announced the nomination of former Sen. Chuck HagelCharles (Chuck) Timothy HagelIntel chief: Federal debt poses 'dire threat' to national security Hagel: Trump is 'an embarrassment' Tax cut complete, hawks push for military increase MORE (R-Neb.) to replace Panetta in his second term; it is unclear whether Karzai and Hagel will meet at any point.

The relationship between Obama and Karzai has been strained at times, although both leaders insisted in May that reports of discontent were exaggerated. At the meeting, Karzai called relations "strong and well-rooted," although he admitted to "moments" where he and Obama "speak frankly to each other." By contrast, President Obama called tensions "simply overstated."