Pakistan had brokered the first round of direct talks between the fragile Afghan government and Taliban in Islamabad in July 2015.
The Afghan President received Abbasi at the Afghan Presidential Palace.
The ministry said the Prime Minister will have in-depth consultations with Ghani and Afghan Chief Executive Abdullah Abdullah on matters of mutual interest, including strengthening bilateral political, economic, security and counter-terrorism cooperation, returning Afghan refugees, combating drug production and illegal drug trade, the Afghan peace process and the regional political and security situation.
Abbasi was welcomed by President Ashraf Ghani and his cabinet members when he arrived at the Presidential Palace at around 10:50am Kabul time.
Pakistan Prime Minister Shahid Khaqan Abbasi will travel to Afghanistan on Friday on a day-long visit during which he is likely discuss a range of issues, including ways to facilitate talks with the Taliban.
Ghani called stability the key to regional peace, saying decisions by leaders of the two countries could guarantee the security and prosperity of their coming generations.
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Pakistan urged Afghanistan to focus on taking effective counter-terrorism actions including plugging of large gaps existing along the Afghan side of Pakistan-Afghanistan border to prevent the targeting of Pakistani civilians and security forces by terrorists from Afghan soil. "The Prime Minister will also meet senior Afghan political leaders", read the statement.
Abbasi recently joined the Afghan president in Herat to inaugurate the TAPI gas pipeline project.
They have made a decision to operationalize the five working groups under "Afghanistan Pakistan Action Plan for Peace and Solidarity".
Pakistan also aspires to deepen people to people contacts. The need for strengthening regional connectivity and energy supply from Central Asia to Pakistan via Afghanistan also figured at the meeting.
It was during his meeting with Janjua that Ghani invited Abbasi to Kabul to "initiate a state-to-state comprehensive dialogue".