A similar e-mail was sent to news channels by the Indian Mujahideen group after blasts in the western city of Jaipur in May which killed more than 60 people.
The attack in Ahmedabad - Gujarat state's commercial capital - came a day after several devices went off in the southern city of Bangalore.
The government has deployed an extra 3,000 security personnel in Delhi, and other cities are on alert, including Mumbai and Jaipur.
Home Secretary Shivraj Patil said the priority was to enable the people of Gujarat and other states to get on with their lives as usual.
"Most important thing today... is to see that the peace and tranquillity in Gujarat is not disturbed, or peace and tranquillity in any part of the country is not disturbed," he said.
"The state governments have been taking steps to see that there are no mischiefs perpetrated by the people and nothing is done to disturb the peace and tranquillity."
The bombs in Ahmedabad were detonated with timers in two phases, the first at about 1830 (1300 GMT), officials said. The second series of explosions caught some victims and their helpers arriving at hospitals.
At least two unexploded bombs were later defused in Ahmedabad and sent for forensic examination.
Another two unexploded bombs were also found in the nearby city of Surat.
The BBC's Zubair Ahmed said he saw about 60 people - some in a serious condition - being treated in a large hall at one of the hospitals in Ahmedabad.
They were surrounded by family and friends, many of whom were angry, saying the bombers wanted to cause a rift between Hindus and Muslims.
A doctor said they had been treating bomb blast victims when there was an explosion outside the hospital, after which there was chaos.
He said the whole building shook and the road outside was covered in blood.
In a statement on her website, President Patil "expressed her heart-felt condolences for the loss of life and urged the people of Ahmedabad to remain steadfast in this testing time and maintain peace and harmony".
Appeal for calm
Prime Minister Manmohan Singh also condemned the attacks, and urged people to remain calm and maintain communal harmony.
Hospitals treating the injured were also targeted in the attacks
Narendra Modi, the controversial chief minister of Gujarat, said the "land of Mahatma Gandhi has been bloodied by terrorists whom we shall not spare".
"Terrorists are waging a war against India. We should be prepared for a long battle against terrorism," he warned.
Mr Modi has been accused of failing to protect Muslims in the riots in Gujarat during 2002 in which at least 1,000 people died, including many in Ahmedabad. The violence erupted when a fire broke out on a train carrying Hindu pilgrims, killing at least 59 people.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.