People were seen flocking to local shops to buy essential items and Christmas goodies and gifts.
Many people faced difficulties in transferring money electronically due to the ban.
The internet services were suspended on December 11 after major protests had erupted across the state over the amended citizenship bill.
Association for hearing, speech-impaired in Assam files complaint with rights panel over internet shutdown
In its complaint to AHRC, the Assam Association of the Deaf alleged that the suspension of internet services 'violates rights of people' from the deaf community and others.
The curfew was relaxed from 6 am in areas under Lumdiengjri police station and Sadar police station limits, an order issued by East Khasi Hills District Magistrate M W Nongbri said.
The top cop of Assam Police said that the situation is normal and no violence was seen in the last few days.
The decision to lift the curfew in Guwahati was taken at a law and order review meeting chaired by Chief Minister Sarbananda Sonowal on Monday.
Night curfew in Guwahati, however, will continue to be in force, Assam Police Chief Public Relations Officer Rajiv Saikia informed the media.
In some relief to residents, markets at many places were open till 6.00 pm and prices of vegetables and fruits came down a bit compared to the rates a day before.
The Chief Minister had on Saturday also appealed to the people of the state to maintain peace and harmony with regard to protest against the Act.
Ishwar Nayak, who sustained bullet injuries during the violence in Guwahati, succumbed to his wounds at the Gauhati Medical College and Hospital.
Long queues were seen outside shops at several places, including Dispur, Uzan Bazar, Chandmari, Silpukhuri and Zoo Road in Guwahati town.
Sam was injured in the incident which took place at Namghar street intersection on Thursday.
People also queued before ATMs across the city to withdraw cash, but most of the machines have dried up.
No clashes between security personnel and protesters were reported in the city. However, sporadic incidents of road blockades in the city were reported in the morning.