Officers sweeping the area screened other suspicious packages in the vicinity, but officials said they did not discover any other explosives.
Richard Martin, 8, of Boston's Dorchester neighborhood was identified as one of the three dead. His 6-year-old sister had a leg amputated and their mother suffered serious head injuries.
Race officials said the boy had just hugged his father after he crossed the finish line, and was returning to where the sister and mother were standing a short distance away when a bomb exploded.
Six Boston hospitals treated the injured, several of whom were in critical condition. A doctor at Massachusetts General Hospital, where 30 of the victims were taken, said most of the serious wounds involved burns and lower body extremities.
Dr. George Velmahos, chief of trauma surgery at Mass General, said some patients withstood 40 or more pellets, nail-like fragments and other sharp objects that were likely packed into the bombs.
Liz Norden of suburban Wakefield told the Boston Globe that two of her sons, both in their 30s, each had a leg amputated from the knee down.
President Obama, speaking on national television Monday night from the White House, assured the nation "we will find who did this and we will find out why they did this. Any responsible individuals, any responsible groups will feel the full weight of justice."
Investigators said they did not know if the bombings were connected in any way to the marathon being run on Patriots Day, a state holiday in Massachusetts to commemorate the start of the Revolutionary War with the battles of Lexington and Concord more than 235 years ago. It was also noted that Monday was the deadline for filing federal taxes.
The marathon is an iconic Boston event, attracting elite runners from across the world. Lelisa Desisa of Ethiopia won the men's division Monday, and Rita Jeptoo of Kenya the women's division. Both finished more than two hours before the bombing.
Details for this story were provided by the FBI, Massachusetts State Police and Boston Police Department.