Biden said at the beginning of the meeting on Friday that "our troops may be leaving but support for Afghanistan is not ending in terms of support and maintenance of helping maintain their military as well as economic and political support".
"Afghans are going to have to decide their future, senseless violence has to stop," he continued.
On his part, Ghani paid tributes "to the 2,448 Americans who paid the ultimate sacrifice, over a million American veterans who have served with honour and dignity for your security and our freedom".
He added that "Biden's decision has been historic. It has made everybody recalculate and reconsider. We are here to respect it and support it".
"We are entering into a new chapter of our relationship where the partnership with the US would not be military, but comprehensive, regarding our mutual interest. And we're very encouraged and satisfied that this partnership is taking place," Ghani further said.
Regarding the security situation, Ghani said that on Friday the Afghan Defense and Security Forces have retaken six districts, both in the south and the north.
"It's showing our determination."
The two Afghan leaders also met House Speaker Nancy Pelosi and Secretary of Defense Lloyd Austin earlier, reports Xinhua news agency.
The White House later said in a statement that the US will provide Afghanistan with critical emergency medical assistance and 3 million doses of Covid-19 vaccine through the WHO-led COVAX initiative.
Biden had requested over $3.3 billion of security assistance for the Afghan military next year, and other forms of financial support will also continue, according to the statement.
Taliban militants have been continuing heavy fighting against government forces since the drawdown of US troops on May 1.
The Taliban, according to its spokesman Zabihullah Mujahid, has captured more than 70 districts over the past month.
In the latest development, it occupied Khash district in Badakhshan province on Wednesday.
The Biden administration plans to relocate thousands of Afghan interpreters and others, who worked with the US military and feared Taliban reprisals, to safe locations as they wait for their application for entry to the United States to proceed.
Despite the grave situation on the ground, the Pentagon said earlier this week that it was still committed to the September deadline set by Biden.
Biden announced in April that all US troops would leave Afghanistan before September 11, the 20th anniversary of the 9/11 attacksThe Associated Press reported Thursday that the main portion of US forces would complete its withdrawal in the next two weeks, and around 650 troops are expected to remain in Afghanistan to provide security for diplomats.