Of the new cases, 777 were reported from Guwahati city alone.
"In the biggest spike ever, Assam on July four reported 1202 cases, 777 of these from Guwahati city alone. Time for all of us to be vigilant," the minister tweeted.
Of the 11,001 cases, 4,657 are active, 6,327 have recovered, 14 have died and three have migrated out of the state, he said.
Meanwhile, the state government has given certain relaxations in the 14-day complete lockdown in Kamrup (Metro) district, under which Guwahati city falls, by allowing grocery shops to open on alternate days for two days from June 5.
Sarma on Saturday donned a PPE kit to visit a COVID-19 ICU ward at the Guwahati Medical College Hospital to inquire about the health of critical patients.
He said the doctors were taking admirable care of the patients.
"To enquire health of patients I went to #COVID19 Ward ICU at GMCH, after putting on PPE kit. Doctors are taking admirable care of patients including providing dialysis etc. Patients say they feel enormously protected. Such dedication can be for nothing else but for humanity," the minister tweeted.
He also visited the newly inaugurated COVID Care hospital at Khanapara field, Guwahati, to review treatment facilities and interact with patients admitted there.
Sarma said he advised the doctors to maintain a constant vigil and take proper precautions and care.
Meanwhile, the Raj Bhawan campus and its surrounding areas in Guwahati City were sealed and declared a containment zone two persons of the Governor's Office tested COVID-19 positive, an official said.
Assam Governor Jagadish Mukhi, his wife Prem Mukhi and 176 employees, including security personnel deployed at the Raj Bhavan and their family members, were tested on July 1 after two personal security officers had tested COVID-19 positive earlier.
Among those tested on July 1, two staff members were found to be positive while the results of the others, including that of the governor and his wife, are awaited.
The state has so far tested 4,49,629 samples for the disease.
At present, 13,040 people are in institutional quarantine in Assam, while 1,28,247 are in home-quarantine, a state government bulletin said. DG IJT