Relations between the two nations have been strained, with Karzai refusing to sign a security agreement which would allow some American troops to remain in Afghanistan after 2014.
Obama said during his yesterday speech that a small US military force may remain in Afghanistan next year but didn't say how many.
Karzai noted in a statement today that Obama had not set a timeline for signing any deal, calling that "positive."
He urged an end to "negative propaganda" against Afghanistan and said he now believes the two countries can work together to help restart Afghanistan's peace process.