Karzai said an Afghan delegation, headed by the country's foreign minister, Rangin Dadfar Spanta, would visit the United States as part of the review.
He made the comments during a joint news conference with Obama's special envoy to Afghanistan, Richard Holbrooke, who is on a fact-finding trip to the region that began on Thursday.
The U.S. is studying the situation in Afghanistan at a time of worsening violence.
The U.S. is contemplating sending up to 30,000 more troops to the country to bolster the 33,000 already in Afghanistan.
Holbrooke said that Mr. Obama welcomed Karzai's suggestion that Afghanistan join the review in a letter Karzai recently sent to the U.S. president.
Mr. Obama's new envoy to Afghanistan also said the United States supported the Afghan electoral commission's decision to hold elections in the country in August.
Holbrooke said he hoped a high-level U.S. delegate would visit Afghanistan every month, "to represent the United States, our new president, our continued policy of support and to find ways to improve our joint effort".
Holbrooke's visit to the country comes amid a downturn in U.S.-Afghan relations and an upswing in violence.
Karzai said on Saturday he still had not spoken with President Obama almost a month after his inauguration, a sign the Afghan president no longer enjoys the favored status he had under former President George W Bush.
U.S. Special Operations Forces conduct targeted night raids against known militant leaders, but the operations have resulted in many Afghan civilian deaths, an issue that has increasingly angered Karzai.
Mr. Obama has said the U.S. will increase its attention on Afghanistan under his tenure as the U.S. transitions out of Iraq.
But the administration is still debating how to stem the rising Taliban tide and tackle the endemic corruption in Karzai's government more than seven years after the 2001 invasion.