His remarks came weeks after US President Donald Trump called on Pakistan to do more to eliminate militant sanctuaries, a long-standing demand by Washington.
"We are open for joint patrolling, we are open for joint posts" along the border with Afghanistan, Abbasi was quoted as saying by Dawn online on Wednesday.
"We will put up a fence there; the Afghans are welcome to put up another fence on their side," he said.
"If you want statistics, there is much more happening across the border from Afghanistan than anything that happens from Pakistan into Afghanistan."
"All the criminal elements we are fighting are based in Afghanistan," Abbasi said.
Trump called on Pakistan to eliminate militant sanctuaries in a speech last month laying out a new South Asia strategy to try and win the 16-year-old war in Afghanistan.
Abbasi said his government had yet to receive any specific demands from the Trump administration, adding that Pakistan would act on any information shared by US authorities.
He denied that Pakistan supported militant groups as he batted away suggestions that Trump's comments would upend relations between the Cold War allies.
"We don't think the Pakistani-US relationship will be defined by Afghanistan," the Prime Minister said.
"This relationship (is) 70 years old (and) cannot be redefined by one issue or it should not be redefined by one issue," Abbasi said.
When asked about US plans to get tough on Pakistan and cutting billions of dollars worth of military and financial aid, the Prime Minister said: "We have nothing to hide, as a general rule you do not punish allies. We are open (with the US). We are transparent."
Abbasi said that the US had not clarified some of the perceptions that were created after Trump's policy statement on Afghanistan and South Asia.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)