When asked about the US' remarks that it wants to see de-escalation between Pakistan and India, Faisal said, We have welcomed these statements by the USA officials since Pakistan has also been making consistent efforts to reach out to India with a view to lowering the temperatures.
Asif was quite vocal in criticising U.S. for hiding its failures.
While giving a rundown of his visit to Pakistan last week, Tillerson informed that Pakistan has indicated to act against terrorists, if given information regarding their whereabouts.
The spokesman further clarified that Pakistan has always emphasised the need of "Afghan-owned" and "Afghan-led" efforts for bringing lasting peace and stability in Afghanistan.
Mr Tillerson said that it was in the interest of Pakistan to change its "long-standing" relationship with terrorist organisations.
Asif said that Pakistan was ready to play its due role in restoration of peace in Afghanistan through the platform of the Shanghai Cooperation Organisation (SCO).
Tillerson, who also visited Afghanistan and India last week, responded to questions on Pakistan's co-operation in the fight against terrorism in the aftermath of US President Donald Trump's South Asia Policy.
"We reject baseless allegations of safe havens and have repeatedly conveyed to the United States leadership that it should refrain from making unfounded assertions", said Mohammad Faisal, the new spokesman who took over from the outgoing Nafees Zakaria.
"If America frames its policy free from the influence (of army generals), it will be much more successful and effective".
The minister said that the concerns expressed and suggestions made by the lawmakers would serve as a guideline in framing the foreign policy.
The Lashkar-i-Jhanghvi, an offshoot of anti-Shia Pakistani sectarian group, was also named in the list.
When asked about Secretary of State Rex Tillerson's remarks that the USA has given Pakistan another chance to fight terrorist safe havens on its territory, Faisal said Pakistan made significant gains through its effective counter-terrorism operations.
The report further said that the list of 20 terrorist groups includes three types of groups: those indulged in attacks into Afghanistan, those who target attacks in Pakistan and the groups focussed on Kashmir. Harakatul Mujahideen is a Pakistan-based militant group operating primarily in Kashmir. "The US says that group had links to Osama bin Laden and Al Qaeda as well".
"The Kashmir dispute can only be resolved through implementation of relevant UN Security Council (SC) Resolutions, which remained unimplemented to this day, as the people of Indian occupied Kashmir (IoK) have been struggling for the just right of self-determination, as envisaged in the resolutions, from the past 70 years", he said.
The US also identified Lashkar-e-Taiba as one of the largest and most active terrorist organisations in South Asia. This group is also focussed on Kashmir and it was involved in the 2001 parliament attack in New Delhi and 2008 Mumbai terror attacks.