Tsarnaev's lawyers argue that the heavy media coverage of the bombings makes it impossible to find impartial jurors in the Boston area. They also want to delay the start of the trial.
Tsarnaev, 21, and his brother, Tamerlan, allegedly set off two backpack bombs at the marathon finish line on April 15, 2013, choosing a time when the area would be crowded with middle-of-the-pack runners and their supporters. Three people were killed and more than 260 injured.
Tamerlan Tsarnaev, 26, was killed in a confrontation with police a few days later, after he and his brother allegedly killed an officer at the Massachusetts Institute of Technology.
U.S. District Judge George O'Toole gave prosecutors time to respond to the defense change of venue request.
Tsarnaev could be sentenced to death if he is convicted. At the time of the bombing, he was a student at the University of Massachusetts Dartmouth.