"A bilateral trade agreement will add new fuel to the economic revival" seen in Afghanistan since the ouster of the Taliban by US-led forces, Bush said as they made a joint public appearance in the White House Rose Garden on Tuesday.
Earlier, Karzai asked the US Congress for a long-term commitment to rebuilding his country and to give private companies incentives to invest there.
Receiving several ovations at a joint meeting of the House of Representatives and the Senate, Karzai said the US and Afghanistan "must enhance our strategic partnership. The security of our two nations is intertwined".
Karzai told US lawmakers that enhancing prospects for stability and democracy would require "sustaining and accelerating the reconstruction of Afghanistan through
long-term commitment, and providing incentives to the private sector for investing in Afghanistan".
The US so far has committed about $2.2 billion to rebuild Afghanistan, an amount some lawmakers have criticised as too low and a result of the Bush administration's emphasis on Iraq where $18.6 billion has been committed for reconstruction.
"To succeed, we ask for your continued investment. Afghanistan is open for business and American companies are most welcome," Karzai said, and cited the country's potential to produce hydro-electricity and reserves of minerals, oil, natural gas and coal.
The US-sponsored government is facing continuing resistance in the fractured country with daily attacks on troops and officials.
On Monday Hamid Agha, head of immigration in the city of Kandahar, was shot dead, Aljazeera's correspondent said.