An ABC News/Washington Post telephone poll of 1,002 people conducted July18-21 found that 53 percent support charges against Snowden, up from 43 percent in June.
At the same time, the poll found 71 percent of people who think Snowden's disclosures harmed national security are in favor of criminal charges.
More than half of those polled indicated they opposed economic retaliation against any country that provides asylum to Snowden, ABC News said.
A Wall Street Journal/NBC News poll of 1,000 U.S. adults conducted July 17-21 found only 11 percent currently view Snowden in a positive light while 34 percent said they view him negatively, The Wall Street Journal reported.
Nearly a third said they didn't know who he was, the Journal said.
The poll carried a margin of error of plus or minus 3.1 percent.
The ABCNews/Washington Post poll, conducted in both English and Spanish, carried a margin of error of 3.5 percentage points.