In the delegation level talks in Kabul, the two sides agreed to continue talks, an official statement said.
Abbasi is on a one-day visit to Afghanistan on Ghani's invitation, having arrived earlier on Friday.
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.
In a statement, the Foreign Office said Abbasi was visiting Kabul on an invitation of Afghan President Ashraf Ghani.
The PM, accompanied by several other top Pakistani officials on the trip - his first to Kabul since becoming prime minister previous year - will hold meetings with a string of Afghan officials, according to Ghani's spokesman, Shah Hussain Murtazawi.
Pakistan and Afghanistan share strained bilateral relationship.
During his stay in Kabul, Abbasi also met with senior political leaders, including Gulbadin Hekmatyar, Ustad Mohammad Mohaqiq, Ustad Mohammad Karim Khalili, Pir Sayed Hamed Gailani, to convey the support of the government and people of Pakistan to all ethnic groups in Afghanistan and underscore Pakistan's commitment to peace and stability in Afghanistan.
The visit, aimed at reducing tensions between the two neighbouring countries and further strengthening the Afghan peace process, comes in the backdrop of allegations by authorities in Afghanistan.
Accusations that Islamabad's powerful military and intelligence services have considerable influence over the Taliban make it unlikely that Afghanistan will have much success in pushing for Pakistan to boost security and counter-terrorism operations along their shared border.
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.