The explosions went off near 671 Boylston on opposite sides of the street near Copley Square around 2:50 p.m., about halfway through the race.
The dead included an 8-year-old boy, The Boston Globe reports.
"The American people will say a prayer for Boston tonight," said President Obama in brief nationally televised remarks.
The president said officials "still do not know who did this or why" but that once those responsible are identified they will "feel the full weight of justice."
One unidentified man was being questioned by authorities.
"The FBI-led Joint Terrorism Task force of federal, state and local officials are interviewing an injured male seen running from the scene," a federal homeland security official tells PEOPLE.
Brian Walker, a 49-year-old engineer, was an eyewitness at the scene.
"I was fifty feet from the explosion and taking pics of the race and I heard two explosions. Five seconds apart. And it was so powerful that it almost blew my hat off my head. It sounded like a cannon. You could feel the blasts hit your body," he told PEOPLE.
Walker continued, "People were screaming. After the second explosion, everyone started screaming and running. People were pushing over the barricades and trying to get over the barricades and escape and so I went closer to the explosion to see if I could help and I took pictures as I was running. There were unbelievable injuries."
"I saw horrific injuries. There were people who lost limbs and people who were bleeding all over the sidewalk. Like out of war zones. I saw two people who lost a leg. Cut off from the knee. One woman – they were trying to keep her alive and she was having trouble breathing," he added.
In an afternoon press conference, Boston Police Commissioner Ed Davis confirmed a third incident at the JFK Library – a fire in a trash barrel, according to a source – but it wasn't known if it was related.
In the meantime, the Red Cross has established a website to assist runners and family members in locating each other in the city.
The Boston Police Department asks that families of victims please call 1-617-635-4500. Eyewitnesses or people with information should call 1-800-494-TIPS.
John Tlumacki / The Boston Globe / Getty