Hafiz Saeed, who carries a USD 10 million bounty on his head for his role in terror activities, has been under house arrest in Pakistan since January this year.
Mr Asif told senators during a session of the parliament's upper house that the US has "handed over a list of 75 militants while we gave them a list of around 100 terrorists."
The list was passed on during the maiden visit of US Secretary of State Rex Tillerson to Pakistan on Tuesday.
"The Haqqani network is on the top of the (US) list but none of the militants are Pakistanis," Mr Asif told senators.
Saeed, a Pakistani citizen, headed the JuD which was listed as a foreign terrorist organisation by the US in 2014.
The JuD is the front for the banned Lashkar-e-Taiba (LeT) terror outfit which is responsible for numerous terror attacks in India, including the Mumbai terror strike of 2008.
The Afghan-based Haqqani network has carried out a number of kidnappings and attacks against US interests in Afghanistan. The group is also blamed for several attacks against Indian interests in Afghanistan, including the 2008 bombing of the Indian mission in Kabul that killed 58 people.
The US, Mr Asif said, had made a habit of handing over lists of wanted people to Pakistan, which traded them for favours - a matter that needed to be debated.
"Neither are we supporting them (Afghan Taliban), nor do they need our help," Mr Asif said.
"Somebody else is sponsoring them now," he added, without elaborating on it.
Mr Asif asserted that many of the key Taliban names were now shadow governors in Afghanistan or no longer alive.
During his meeting with the Pakistani leaders, Mr Tillerson renewed the US demand for tough action against the Afghan Taliban and the Haqqani network.
Mr Asif said the meeting with Mr Tillerson was held in cordial atmosphere and there was no accusations from either side.
"We clarified to the visiting dignitaries that Pakistan will not indulge in any kind of proxy war but will continue to play its role for peace and security in the region," he said.
Mr Asif said Pakistan wants to expand relations with the US on the basis of equality and self-respect.