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Gallup said that most striking was how those surveyed seemed to think there was little that could be done.

“It is clear that Americans are not overwhelmingly convinced that any of the actions would be highly effective in preventing future school shootings,” the polling organization said.

Administration officials said this week that the president supports reinstating a ban on assault weapons, but only as part of a much broader strategy aimed at putting a stop to the string of mass shootings that the nation has endured in recent years.

Given the renewed attention on Capitol Hill to firearms restrictions in the wake of Friday’s slayings, the main focus of the task force likely will be more gun-control measures. But Mr. Obama said the group also would examine mental health issues and “a culture that — all too often — glorifies guns and violence,” he said.

Retiring Sen. Joe Lieberman, Connecticut independent, this week called for a similar commission to study contributing factors to gun violence, singling out the entertainment world and “realism of video games and movies now” as a direct link to the shooting sprees.

The president said he chose Mr. Biden to lead the task force at least in part because of his role in drafting the comprehensive 1994 crime bill, which included a ban on assault weapons. That ban lapsed in 2004.

During his remarks, Mr. Obama spoke favorably about the ban, noting that President Reagan supported it. He also referred to proposals to enhance background checks for gun sales and places limits on purchases of high-capacity magazine clips.

While some pro-gun lawmakers on Capitol Hill have started expressing support for more restrictions, the gun lobby remains a powerful force in Washington.

On Tuesday, the National Rifle Association said it was “heartbroken” by the tragedy and wants to play a role in a national conversation to limit gun violence.

The funerals in Newtown scheduled for Wednesday included those for four children, a teacher and the principal of Sandy Hook Elementary, the school that 20-year-old gunman Adam Lanza attacked Friday.