Abbasi met CPN (Maoist Centre) Chairperson 'Prachanda' in the capital and the two leaders discussed relations between Nepal and Pakistan, Nepalese media reported.
After the meeting, Prachanda said that matters related to bilateral relations and mutual interests were discussed in the meeting.
During the 45-minute meeting, they also discussed measures to improve bilateral trade and economic relations, Republica newspaper reported.
Prachanda said the meeting also stressed the need of initiative from all member-states to revitalise the South Asian Association for Regional Cooperation (SAARC).
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Abbasi also paid a courtesy call on President Bidya Devi Bhandari and addressed a programme organised by the SAARC Secretariat.
During a meeting with SAARC Secretary General Amjad B. Sial, Abbasi said SAARC was an important forum which required serious and sincere efforts by member countries to explore its true potential.
Pakistan was committed to playing a constructive role in SAARC, the prime minister said.
SAARC member states include Afghanistan, Bangladesh, Bhutan, India, Nepal, the Maldives, Pakistan and Sri Lanka.
Abbasi yesterday met his Nepalese counterpart K P Sharma Oli here and discussed bilateral ties besides ways to revive the SAARC process.
They agreed to enhance cooperation in areas of economy, defence and culture, Pakistan's official APP news agency reported.
Abbasi said Pakistan supported Nepal's unity, sovereignty and territorial integrity as a matter of prime importance.
He said it was heartening that the democratic process in Nepal was flourishing and emphasised that political stability was a key to economic development.
Abbasi is the first high level foreign leader to visit Nepal after Premier Oli assumed office last month.
This was the first official bilateral visit by any Pakistan Prime Minister to Nepal after a gap of 24 years.
In 1994, the then prime minister Benazir Bhutto travelled to Nepal on a bilateral visit.
Former premier Nawaz Sharif had visited Nepal to attend the 18th SAARC Summit in 2014.
Abbasi left for Pakistan this afternoon after wrapping up his two-day Nepal visit.