Obama wearily mourned the victims while speaking at the White House.
"We are confronting yet another mass shooting, and today it happened on a military installation in our nation's capital," Obama said.
There were conflicting reports on which guns Alexis used or how he obtained them.
Two law enforcement officials told The Associated Press that an AR-15 assault rifle was found at the scene, but one of them said Tuesday that Alexis did not use that weapon in the shootings. The official said that guns Alexis used included a shotgun he had purchased and two handguns he took from law enforcement at the scene.
The White House on Tuesday criticized lawmakers who oppose legislation to tighten gun laws.
White House press secretary Jay Carney said Obama "has not ... hidden his displeasure and disappointment in Congress for its failure to pass legislation that's supported by 80-90 percent of the American people."
Carney said the problem lies "overwhelmingly" with opposition Republicans.
About 50 activists from the Connecticut town where the December shooting occurred were on their way to Washington on Tuesday to lobby lawmakers for tougher gun control laws. The trip had been planned before Monday's attack.
The nation's top gun lobby, the National Rifle Association, declined to respond to requests for comment Monday. The group successfully fought Obama's push for stricter firearms laws.
Dan Gross, President of the Brady Campaign to Prevent Gun Violence, said in a statement, "While it is too early to know what policies might have prevented this latest tragedy, we do know that policies that present a real opportunity to save lives sit stalled in Congress, policies that could prevent many of the dozens of deaths that result every day from gun violence."
___
Associated Press writer Nedra Pickler contributed.