Presiding over a high-level meet at the Prime Minister House, Sharif said the doors to dialogue would be kept open but he would not resign from his post, sources said.
The meeting agreed to speedup the process of establishing contacts with political forces, sources added.
Cricketer turned politician Imaran Khan, the PTI chief, has claimed that the 2013 elections were rigged and that Sharif has a "fake mandate".
Meanwhile, as a protest march continued in Pakistan, Interior Minister Chaudhry Nisar Ali Khan on Tuesday announced the army has been entrusted with the responsibility of securing Islamabad's sensitive Red Zone area.
The move came as protesters from Imran Khan's PTI and the PAT persisted with their threat to march to Constitution Avenue in the federal capital city, a Dawn report said.