President Donald Trump has vowed to get tough with Pakistan unless it changed its behaviour, with USA officials threatening further reductions in aid and mooting targeted sanctions against Pakistani officials.
"We are committed in the war against terror", he told Tillerson.
US Secretary of the State said that Pakistan is an important country in the region. "And we are looking forward to moving ahead with the USA and building a tremendous relationship".
"We have made some very specific requests of Pakistan in order for them to take action to undermine the support that the Taliban receives and the other terrorist organisations receive in Pakistan", Tillerson said.
In August, President Donald Trump unveiled his policy for Afghanistan and South Asia.
In Afghanistan on Monday, he told reporters that Pakistan's co-operation on counterterrorism is essential for a good relationship with the U.S. His comments echoed those of other top U.S. officials who have been pressing Pakistan on the matter.
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U.S. and Pakistani sources say Tillerson's visit to Islamabad will be followed later in the year by Defense Secretary Jim Mattis as Trump seeks to send a tough message to the wayward Cold War ally.
After Tillerson's meeting with Ghani on Monday, the American Embassy and Ghani's office released a statement claiming that the two men had met in Kabul.
As one of 16 "Non-Nato Major Allies", Pakistan benefits from billions of dollars in aid and has access to advanced USA military technology banned from other countries.
The rescue was followed by drone strikes on both sides of the Afghanistan-Pakistan border targeting long-time foes of both Washington and Islamabad.
Pakistan's prime minister pledged his country's cooperation in fighting militants during talks Tuesday with Secretary of State Rex Tillerson, who has repeatedly said Pakistan must do more to curb support for terrorist groups. As the New York Times reports, the red fire alarm and military-style clock indicated the meeting took place not in Kabul but at the United States military base in Bagram, more than 30 miles away.