The visit comes against the backdrop of Islamabad's support for Mr. Ghani's offer of peace talks with the Taliban.
PM Abbasi was welcomed by Afghan President Ashraf Ghani and the two inspected an honor guard at the Presidential Palace in Kabul before heading in for meetings.
During his visit, PM Abbasi will have in-depth consultations with Afghan President Ashraf Ghani and Chief Executive Dr Abdullah Abdullah on matters of mutual interest, including strengthening bilateral political, economic, security and counter-terrorism cooperation, return of Afghan refugees, combating drug production and narco-trade, Afghan peace process and regional political and security situation.More news: Journalist accreditation order withdrawn
Pakistan said it aspires to deepen people to people contacts.
He will also meet senior Afghan political leaders.
Abbasi had earlier visited Afghanistan in February this year to inaugurate the TAPI gas pipeline project.
They also discussed Pakistan's connection to the Central Asia, energy transition, Quetta-Kandahar-Herat and Peshawar-Jalalabad railroad projects and construction of Peshawar-Jalalabad highway.More news: Gay dating app Grindr to stop sharing HIV status with analytics firms
Pakistan has rejected "baseless Afghan allegations" of violation of its airspace and air raids inside Afghan territory by the Pakistan Air Force.
She noted the meaningful role that Pakistan, partnering with the United States, could play in achieving a peaceful resolution in Afghanistan, a press release by the U.S. embassy had said.
He added that in a meeting of the director generals military operations of the two countries held in Rawalpindi on Thursday, Pakistan had shared details of the operations with the Afghan side indicating that these operations were on the Pakistani side of the border.
Since then, several attempts have been made, with little success, to resume the stalled peace process by a four-nation group comprising of Pakistan, Afghanistan, the USA and China.More news: Trump conjures a new immigrant rape epidemic
It was during his meeting with Janjua that Ghani invited Abbasi to Kabul to "initiate a state-to-state comprehensive dialogue".