Mr Biden pledged technical support for a referendum due early next year.
NAIROBI, 10 June 2010 (BBC) - The pair discussed a referendum due next year when the semi-autonomous southern region will be given the chance to vote for full independence.
A Sudanese official said that Mr Biden pledged US technical and financial support for the referendum.
Mr Kiir, who won polls in April, is the first elected president of the region.
The elections were part of a peace deal that ended a 21-year civil war between the north and south.
The BBC's Will Ross in Nairobi says there are fears that key issues will not be resolved in time for the referendum and there are claims of rising tension between the north and south of Sudan.
If the vote takes place, the people of Southern Sudan are almost certainly going to choose to break away from the Arab dominated north, our correspondent adds.