Since arriving on Sunday, Ghani has been feted by the Obama administration and is due to address Congress on Wednesday. The welcome contrasts sharply with frosty relations that developed between Washington and Ghani's predecessor Hamid Karzai.
Ghani thanks US military
Ghani has repeatedly expressed gratitude to the American military and at the White House spoke about meeting the widow of Major General Harold Greene, the highest-ranking US officer killed during the 13 years Americans fought in Afghanistan.
"The 2,215 Americans that have died, must not die in vain. They must leave behind a legacy of a stable Afghanistan," Ghani said.
Some US lawmakers had also called for a slower drawdown of troop levels. US Representative Mac Thornberry, a Republican who leads the House of Representatives Armed Services Committee, said the decision announced on Tuesday was "appropriate."
"Iraq has shown us the consequences of leaving a fragile ally too early," he said in a statement. "The bottom line is that our own security is at stake."
Ghani and Afghanistan's Chief Executive Abdullah Abdullah met at the presidential retreat at Camp David on Monday with top US officials including Defense Secretary Ash Carter, who said Washington would fund Afghan security forces at least into 2017.
On Thursday will travel to the United Nations to meet Secretary General Ban Ki-moon.