Mr Morrison was due to visit his Indian counterpart,Narendra Modi,from January 12 to 16 but said on Friday afternoon he was"inclined not to proceed". A planned trip to Japan,which Mr Morrison was due to visit on his way back to Australia,is also in doubt.
He has also cancelled plans to attend the Sydney Test cricket match over the weekend,a traditional prime ministerial engagement,and will instead be in Sydney and Canberra receiving briefings.
He said members of the NSC,which includes Mr Morrison,Nationals leader Michael McCormack,Treasurer Josh Frydenberg,Foreign Minister Marise Payne and Defence Minister Linda Reynolds,would convene on Saturday morning ahead of another scheduled meeting on Monday. He would make a formal decision on whether to travel overseas following those discussions.
"I'm inclined not to proceed on that visit. There are issues I need to resolve formally when working through issues of that nature. That is my inclination on that issue,"Mr Morrison said.
Mr Morrison has flagged the role of the Defence Force would become"greater and greater"in the days ahead through air evacuations,engineering support,accommodation and evacuation centres.
"We'll be running that on a daily basis on a very close watch. And I think Australians can be confident of that being the case,"he said.