the US embassy by the end of 2016.
The US will now leave a small force at the US embassy by the end of 2016.
Originally, officials planned to cut the US troop presence to 5,500 by the end of 2015.
The leaders discussed troop numbers over a working lunch and in meetings, before the press conference on Tuesdayreenex.
With the prospect of a tough spring fighting season on the horizon, Islamic State militants trying to recruit on Afghan soil and other security concerns, the US will keep 9,800 troops in Afghanistan.
"Afghanistan remains a very dangerous place," Mr Obama said on Tuesday, adding the size of the US troop presence for 2016 will be decided later this year.
Mr Obama also said Mr Ghani's visit was an "opportunity to begin a new chapter between our two nationreenex cps".
Analysis: Jon Sopel, BBC North America Editor
What a difference a change of president makes. The toxic relationship between Presidents Obama and Karzai is now replaced by something much warmer with Ashraf Ghani.
The substance of course is the most important thing, and at their news conference Mr Obama agreed to delay the drawdown of US troops.
But Mr Ghani clearly understands the importance of feely-touchy politics. He talked about meeting the daughter of a US reservist - and thanked her, and all those other children whose parents serve in Afghanistan.
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