The two met at Sharif's private residence in the hill resort of Murree near Islamabad where Sharif has been staying since he vacated the official residence two days ago after the Supreme Court disqualified him over the Panama Papers scandal.
Shehbaz Sharif, who will take over from Abbasi after he is elected to the National Assembly, was also present during the meeting, the Pakistan TV reported.
Abbasi, a die-hard Nawaz Sharif loyalist, was yesterday elected as the interim prime minister by the National Assembly. He was later sworn in by President Mamnoon Hussain.
"Justice demands that 1,000 guilty are set free than one innocent is convicted," Abbasi said.
"It is my firm belief that Nawaz Sharif will return to the seat of premiership," he said.