"We've got other vital leads and will be able to crack down on the masterminds very soon," he said.
A total of 13 explosions struck Assam on Thursday, six of which went off in Guwahati.
One bomb exploded just 100 metres from the official residence of Tarun Gogoi, the state chief minister.
More bombs exploded in the districts of Barpeta, Kokrajhar, Bongaigaon and Tinsukia.
An Indian police officer said on Friday they had detained around 12 people suspected of having links to the blasts.
Singh's arrival in Guwahati on Saturday coincided with a 12-hour shutdown called by the opposition Bharatiya Janata Party and two affiliated groups to protest against the state government's alleged failure to clamp down on attacks.
Shops and businesses were closed while cars were off the roads.
Singh, who represents Assam state in the upper house of India's parliament, visited some of the 300 injured.
"We will not be soft on terror and there will be no compromise on terror," Singh said after visiting the injured.
"Whosoever is responsible for the dastardly act we will take effective measures."
Speaking in the immediate aftermath of the blasts, Himanta Biswa Sarma, a government spokesman, said "the needle of suspicion" pointed to the Ulfa, an Assamese separatist group.
Ulfa, however, denies it had any involvement in the bombings.
Mahanta, the Assam police chief, had cautioned on Friday that the investigation was "at a very preliminary stage".
Nevertheless, he said "we have reason to believe that the militants used PE-3 explosives, a highly plasticised, RDX-based explosive".
In the past two decades, more than 10,000 people have lost their lives to political violence in tea- and oil-rich Assam.