Sharif is in London with his ailing wife Kulsoom, who is suffering from throat cancer and has undergone three surgeries so far.
US intelligence agencies had been tracking the hostages and shared their location when they were shifted to Pakistan.
Maryam, who is being groomed as Sharif's political successor, appeared in the court for the first time on Monday.
The ICJ had asked Pakistan to submit its written response or memorial by December 13 before the court could start further proceedings.
Sharif, 67, had to step down as the chief of the PML-N after he was disqualified as the prime minister by the Supreme Court on July 28 in the Panama Papers scandal.
The court also issued fresh arrest warrants against his children and son-in-law.
Bhutto, the Pakistan Peoples Party chief and a two-time prime minister, was killed along with more than 20 people in a gun and bomb attack in Rawalpindi's Liaquat Bagh during an election campaign rally on December 27, 2007. She was 54.
Pak also suspended all bilateral visits as a mark of protest.
"Our government has invariably made efforts to initiate the process of meaningful dialogue and adoption of peaceful means to resolve the issues but unfortunately the expansionist designs of India have remained the main hurdle in this regard," Abbasi said.
The party, political observers said, seems as an effort to set up a front which is acceptable to moderate Pakistanis.
Musharraf claimed that Nawaz Sharif's India policy was a "total sell out".
Abbasi will be sworn-in in later at a special ceremony at the President's House.
Abbasi will run the government until Sharif's brother Shehbaz is elected as member of parliament
The SC also ordered the National Accountability Court to start a corruption case against Sharif, his sons -- Hussain and Hassan -- and daughter Maryam.
The decision is keenly awaited as it would determine the course of Pakistan's polity and with it Sharif's. An adverse decision may result in Sharif's disqualification, or even snap elections.
Jadhav, 46, filed a mercy petition before Gen Bajwa last month, according to an Inter-Services Public Relations statement issued on June 22. The statement said that the former Indian Navy officer had filed the petition after the Military Appellate Court rejected his appeal.
Sharif said his family business has been targeted for over six decades but "there is no single sentence.
A report in a daily said that Pakistan was worried over the visit as it could have serious implications on strategic stability in the region.
'Nasr' is a high-precision weapon system with the ability to be deployed quickly, the army said.
Addressing the media amid tight security at the Centre Press Club in Muzaffarabad for the first time since the US declared him a "Specially Designated Global Terrorist" on June 27, Salahuddin rejected the US decision and said he was a freedom fighter and not a terrorist.