Last month, the Senate rejected a measure that would have expanded background checks for gun purchases. After the legislation was defeated, and standing before family members who lost loved ones in the Newtown, Conn., school shooting, Obama said he would continue to fight to pass the legislation.

In recent days, Vice President Biden has continued that effort, meeting with law enforcement officials and others to discuss the issue. Next week, a senior administration official said Biden will meet with faith leaders to discuss gun control.

The senior administration official said Friday that Biden "will continue to meet with groups who are active in the gun debate and has said repeatedly and publicly that we aren't going to give up."

"As the president said yesterday, ‘This is just the first round,’” the official said.

Speaking to reporters Friday afternoon as Obama traveled from Mexico to Costa Rica, White House press secretary Jay Carney said Obama is "committed to pressing for action to reduce gun violence and that includes pressing Congress to take action."

"Sometimes these efforts don't succeed initially, but especially when you have 85 or 90 percent of the American people supporting, in the case of background checks being expanded, a legislative proposal, this is going to get done," Carney said.

Carney said Biden would continue to play a "leading role" in the gun effort, "at the President's direction."

The White House spokesman said it's up to gun control advocates to made their voices known and tell Senators that they "let them down."

— This story was updated at 4:13 p.m.