Some areas still hadn't been reached as of midafternoon on Monday, with rescuers battling collapsed bridges, electricity and communication blackouts and damaged roads blocked with debris.
In his post, Mr Shanmugam said that he is now waiting for a flight out of Lombok and thanked everyone for the kind thoughts and prayers.
The Bali and Lombok airports continued operating Sunday night, according to the director general of civil aviation. At the time, killed 17 people, and more than a hundred people were injured of varying severity. At least 82 people were killed and hundreds were wounded, with thousands of buildings damaged.
The quake was centered on the north coast of the island, 48 km northeast of Mataram, its largest city, according to the U.S. Geological Survey.
Sutopo said there were no fatalities among the local and foreign tourists and a joint search and rescue team had deployed three ships to evacuate people.
"And then the roof started falling down on us, rocks and rubble and then just everyone running to get away", he said. "The police officers there were kind", he said, adding that the airport was chaotic, with "lots of people".
Blue tarpaulins dotted the landscape as people prepared to spend the nights outdoors because of aftershocks or because their homes were destroyed.
The main hospital in the town of Tanjung in the north was severely damaged, so staff set up about 30 beds in the shade of trees and in a tent on a field to tend to the injured.
Disaster officials have not said how many people they believe are buried beneath the ruins of the mosque.
Tweets report about the major 7.1 earthquakes in Lombok that triggered widespread panic and a tsunami warning.
A tsunami warning was issued but was lifted after a few hours.
I Made Suprateka, a spokesman for Perusahaan Listrik Negara (PLN), said the state utility company is sending personnel and equipment from East Java and Bali to help restore power in East and North Lombok.
Witnesses said the quake woke up residents and tourists, who ran out of their hotels.
Another strong quake has struck Indonesia's popular tourist island of Lombok.
"We are cutting short our holiday because I can't walk and we're just not in the mood anymore, more in the mood to see our loved ones", said the 26-year-old, sitting on a trolley with his leg bandaged.