"Cabinet will be announced in one to two days," Abbasi told reporters, but did not say why the decision was delayed when arrangements had been made for the oath-taking ceremony today.
Abbasi had met Nawaz Sharif at the ousted former prime minister's Murree residence earlier today. He was accompanied by Sharif's brother Shehbaz, who will take over from Abbasi after being elected to the National Assembly later this year.
Sharif has been staying in Murree since he vacated the official residence two days ago after the Supreme Court disqualified him in connection with the Panama Papers scandal.
The Press Information Department said in a statement that the Cabinet was to take oath at 5:30 pm local time, but it has been postponed.
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The formation of the Cabinet is a challenge for the new prime minister as former interior minister and senior party leader, Nisar Ali Khan, is supposedly not ready to join it.
Khan had announced on Thursday he would resign from Cabinet and parliament after the Supreme Court verdict on Friday.
Khan has accused Sharif of excluding him from his "inner circle" despite a 32-year-long association with the party.
The ruling Pakistan Muslim League-Nawaz (PML-N) is trying to convince Khan to join the Cabinet to put up a united face ahead of general elections next year.
Abbasi would have to find a suitable replacement for Khan if he refuses to join the new government. He would also have to fill the post of minister for petroleum and natural resources which he controlled before his elevation to the top job.
The information ministry had to be run by minister of state Marriyum Aurangzeb during the latter part of Sharif's tenure after Pervaiz Rashid was sacked following the Dawn leaks episode.
There is a strong possibility that Abbasi would appoint a senior party leader as information minister.
There are reports that former railway minister Khawja Saad Rafique, a close confidante of Sharif and party loyalist, may be appointed the information minister.