WASHINGTON - President Obama today suggested that a better background check system for American gun sales might have prevented Monday's mass shooting at Navy Yard that left 13 people, including the gunman, dead.

"Initial reports indicate that this is an individual who may have had some mental health problems," Obama said of the shooter, in an interview with Spanish-language network Telemundo.

Law enforcement records made public today show that Aaron Alexis, a former Navy reservist, had a documented history of paranoia and mental instability. He passed a federal background check and legally purchased a shotgun from a Virginia gun shop on Saturday.

"The fact that we do not have a firm enough background-check system is something that makes us more vulnerable to these kinds of mass shootings," Obama said.

The president has proposed expanding the existing background-check system to cover sales at gun shows and online. He has also sought $20 million for the Justice Department to help encourage states to enter more information - including mental health records - into the system for firearms purchases.

"I've taken steps that are within my control. The next phase now is for Congress to go ahead and move," Obama told Telemundo.

His background check proposal remains stalled in Congress. "We don't have the votes," Senate Majority Leader Harry Reid, a Democrat, told reporters in the Capitol today.

"You have a majority of the American people and even a large percentage of Republicans who are ready to move the country forward, and yet we keep on getting blocked," Obama said in the interview. "And it's a challenge that I'm speaking out on, but ultimately we're also going to need pressure from the public to see if we can change how they do business up there."

Eighty-six percent of all Americans in a May ABC News/Washington Post poll said they support expanded and strengthened background checks for all gun sales. Thirteen percent were opposed.