While 54 percent of Americans say it can be necessary, 45 percent disagree, showed the results of a national survey conducted by The Associated Press and NORC Center for Public Affairs Research at the University of Chicago.
And about half of Americans think it is acceptable to allow warrant-less government analysis of internet activities and communications -- even of American citizens -- in order to keep an eye out for suspicious activity, but about three in 10 are against this type of government investigation.
"In the aftermath of the attacks in Paris and California, we are seeing the public's concern about being personally affected by terrorism evolve. For instance, 20 percent of Americans are very concerned that they or a family member could be a victim of a terrorist attack, up from 10 percent in 2013," said Trevor Tompson, director, AP-NORC Centre.
"The survey also found that respondents are just as concerned about attacks by Islamic extremists as they are about home-grown terrorists," Tompson noted in a statement released on Wednesday.
The survey revealed that only about a quarter of Americans feel protecting their rights and freedoms as citizens is more critical than being kept secure.
While four in 10 of those surveyed said safety is more important than civil liberties, three in 10 said both are equally important.
The survey also revealed that more Republicans favour the analysis of internet activity and communication by the government without a warrant than Democrats and independents.
While Republicans and Democrats are equally anxious about the possibility of being personally affected by domestic terrorism, two-thirds of Republicans and half of Democrats are greatly or somewhat concerned about becoming a victim of Islamic extremism in the US, the findings showed.
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