The PPP yesterday issued the show-cause notice to Rehman, also a former spokeswoman of the party, and suspended the membership of Abbasi, whose wife Naheed Khan was the political secretary of Bhutto.
Rehman and Abbasi, who are both members of Parliament, were issued notices by the PPP for participating in talk shows on the Geo News channel.
The PPP recently decided to boycott the 'Jang' media group, which owns Geo News and The News daily, accusing it of conducting a propaganda campaign against the party and its chief, President Asif Ali Zardari.
Both PPP leaders told the media that they were not aware when and where the decision to boycott the TV channel was taken even though they were members of the party's central executive committee.
Rehman said she had yet not seen the show-cause notice but was in "shock" that speaking on any TV channel could result in violent protests outside her home in Karachi.
A group of women from the PPP stronghold of Lyari protested outside Rehman's residence and burnt her effigy yesterday. The women claimed they were PPP workers but the party distanced itself from the protest.
"As it stands, I had no official communication from the party about any ban on any channel, because I had heard several different (PPP leaders) speaking on all channels, but bizarrely, I am being targeted.
"In the absence of any communication, I followed the Prime Minister's and the President's announcements that we have no war with any media channel," Rehman said.
She said she had been a senior PPP office-bearer and a minister in the current government and had always acted responsibly.
"I have never spoken against my party despite whatever has been done, so I will see what this show-cause is about and certainly respond," she added. Abbasi said he had received a suspension letter from PPP Secretary General Jahangir Badar by e-mail and complained that he was not given sufficient time to reply to a show-cause notice issued on October 20.
Under the party's rules, members should be given a week to respond to show-cause notices but his membership was suspended within 48 hours, he said.
Rehman and Abbasi are among senior PPP leaders who were close to Bhutto and have been sidelined by the current party leadership for the past three years.
Abbasi has often criticised party chief Zardari's actions while Rehman quit the federal Cabinet during the lawyers' movement for the restoration of deposed judges in March last year.