On Monday, Mr. Tillerson held talks with President Ghani at the USA -controlled Bagram Base outside Kabul, while on Tuesday he met the Pakistani leadership in Islamabad.
"We are committed in the war against terror", Abbasi told Tillerson, as the two men sat facing each other on a long table.
ISLAMABAD-U.S. Secretary of State Rex Tillerson is in Pakistan to deliver a tough message on the importance of fighting extremists and driving them from hideouts on Pakistani territory.
"We are committed to the war against terrorism...and we look forward to moving ahead with the USA and building, as you said, an economic relationship", the Pakistani prime minister said in response to Tillerson's comments.
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.More news: Huawei Mate 10 Lite launched with four cameras
In August, President Donald Trump unveiled his policy for Afghanistan and South Asia.
After stopping back in Doha, Tillerson also made an unannounced visit to Iraq on Monday. "And we are looking forward to moving ahead with the USA and building a tremendous relationship", Abbasi replied, according to a pool report. Foreign Minister Khawaja Asif also visited Washington, where he met Secretary Tillerson.
India's External Affairs Minister Sushma Swaraj also called on the visiting dignitary.
But Trump's blistering speech in August accusing Pakistan of harbouring militants saw Islamabad angrily hit back at the claims, insisting the U.S. took no account of the thousands of lives lost and billions spent in fighting extremism.
Tillerson's visit to Afghanistan set social media aflutter Tuesday after Afghan officials released a photo that had seemingly been doctored to disguise the fact that it took place at Bagram, a secure military base, rather than Kabul, which was hit by multiple militant attacks last week. 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.