Shortly after the Senate voted Thursday to proceed on the White House-backed measures, Obama spoke by phone with the families, many of whom have been in Washington lobbying congressional lawmakers.
"The president congratulated the families on this important step forward, noting that the bipartisan progress would not have been possible without their efforts," White House spokesman Jay Carney said.
Carney said Obama told the families he would "keep fighting for the votes they deserve."
The Senate rejected a conservative effort to block debate on the gun control legislation. The 68-31 vote lends momentum to Obama's efforts to crack down on gun violence following the December school shooting in Connecticut. Twenty children and six adults were killed in the shooting.
Carney called the vote "very important," but said it was just the "first stage" in the effort to pass anti-gun violence legislation.