At a meeting with reporters last week, Mr. Azar said that other priorities, like fighting the flu and Ebola, also competed for funds. He did not specify which subjects would be a priority, how much money he might ask Congress to allocate to gun violence research, or whether he will transfer money from other health agency programs.

There is no shortage of ideas — or criticism of the time lost in studying gun violence.

“We have repeatedly and consciously turned our back on the problem,” said Garen Wintemute, a professor of emergency medicine who in July started the Firearm Violence Research Center at the University of California, Davis, with funding from the state. “How many thousands of people are dead today who might have been alive if that research effort had been put in place and we had answered critical questions and set prevention measures in motion?”

It’s a question that haunts researchers. In the aftermath of the Sandy Hook school shooting in 2012, President Obama directed the C.D.C. to reconsider gun violence research. The agency commissioned a report from the Institute of Medicine outlining priorities, but never followed up.

The most pressing questions cited by the institute, now known as the National Academy of Medicine, still have no answers. Who is most likely to use a gun in a crime, and where does the gun come from? How often are guns used in domestic violence cases? How often are the people who are arrested for gun crimes the same individuals who actually bought the weapons?

Then there is a separate set of questions about what kind of policy changes or prevention efforts actually reduce gun-related deaths and injuries.

Andrew R. Morral, a senior behavioral scientist at the RAND Corporation, directed a recent study that found moderate evidence that background checks do reduce both firearm suicides and homicides. The report also said there is moderate evidence that stand-your-ground laws, which allow people to use guns to defend themselves without first trying to retreat, may increase the murder rate.