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His remarks came weeks after US President Donald Trump criticised Pakistan for providing safe havens to militants.
"We are open for joint patrolling (along the border with Afghanistan)," Abbasi said.
Abbasi also referred to fencing of the 2,600-km-long border with Afghanistan, which has already started.
"We will put up a fence there (on our side of border). The Afghans are welcome to put up another fence on their side," he said.
He said that Pakistan was open to bilateral verifications and joint patrols to screen the visitors who cross the border every day.
He rejected the allegations about terrorists' sanctuaries inside Pakistan and said Islamabad was fighting to eliminate militancy.
He claimed the militants were actually based in Afghanistan and carry out cross border attacks in Pakistan.
Abbasi said that Pakistan was ready to work with the US in the fight against terrorism and the two sides should address any concern on the subject through dialogue.
To a question, he said Pakistan had not received any specific demands from the US and would take action if any information was shared.
"We respect other's sovereignty and expect the same from them," he said.
He said the United States had not clarified some of the perceptions that were created after President Trump's policy statement on Afghanistan and South Asia.