In a statement, PM Abbasi said the federal government will extend complete support for development initiatives in the province.
Meanwhile, the country has expressed its "grave concerns" over attempts by New Delhi to "change the demography of Jammu and Kashmir State".
Chief Minister Sindh Murad Ali Shah and Governor Mohammad Zubair welcomed him, reports the Dawn.
Abbasi was sworn in as premier earlier this month. Sindh governor briefed the PM about all the federal projects that are underway.
During the meeting, prevailing situation in Karachi was discussed, PM office media wing said in a press release.
He laid floral wreath at the mausoleum and offered Fateha to pay homage and respect to father of the nation.
Chairing a meeting on law and order in Karachi, the Prime Minister said the federal government is concerned over the recent surge in street crimes in Karachi. He also recorded his impressions in the visitor's book.
Prime Minister Shahid Khaqan Abbasi arrived in Karachi for a day-long visit Saturday, the first time he has visited the city after being elected the prime minister.
The current situation in Karachi was discussed in the meeting.
The prime minister thanked the MQM leaders for voting for him during the election.
It was agreed that all the political forces should combine their efforts to further improve security and business atmosphere in the biggest metropolis of the country.
MQM leader Dr Farooq Sattar had said then that he expected Abbasi to resolve Karachi's issues on a priority basis.
The delegation, comprising its chief Dr Farooq Sattar, Faisal Subzwari, Khalid Maqbool Siddiqui and Kunwar Naveed called on the premier at the Governor's House.