Authorities suspected the separatist United Liberation Front of Asom was behind the attacks, which came less than a week after a deadly blast in Gauhati, the capital of Assam state, said G.M. Srivastava, the state's top police official.
"This is a coordinated attack," said Srivastava.
The blasts occurred on the eve of the 30th anniversary of the founding of the militant group, which has been linked to many acts of terrorism in Assam and usually stages attacks around this time of year.
Suspected militants also threw a grenade at a police station in Udalguri in northern Assam that failed to explode, said senior police official Bhaskar Mahanta.
The first bomb was likely tied to a motorbike and exploded in a crowded market in Gauhati, killing seven people and wounding at least 56, said Srivastava. The blast left several cars on fire amid piles of smoldering wreckage.
After the immediate panic subsided, angry crowds threw stones at police officers who they said were slow to arrive at the scene and had failed to protect the public.
Hours later, a second bomb, this one tied to a bicycle, went off in a market in the town of Dhekiajuli, 130 miles (210 kilometers) north of Gauhati, Srivastava said. At least four people were wounded, he said.
Later in the day, suspected militants threw a grenade at a police station in the town of Mankachar on the India-Bangladesh border, said local police official Bhartha Mahanta. Two police officers were injured, one of them critically, Mahanta said.
A spokeswoman for Singh's office, Deepak Sandhu, said the prime minister's trip had not been canceled.
Srivastava said police had recently received information that the front had been planning a major attack in Gauhati.
The United Liberation Front of Asom wants an independent state for ethnic Assamese and is the largest among dozens of militant groups in the region.
The separatists accuse the government of exploiting the area's natural resources while doing little for the indigenous people - most of whom are ethnically closer to people of Myanmar and China than to the rest of India.
More than 10,000 people have died in separatist violence over the past decade. The March 31 blast in Gauhati left one dead and 13 wounded.
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