Seventy-five percent of Swedes responded that they were "not afraid" of having their phone calls or web surfing monitored, the poll found.
Only 13 percent of respondents to the survey, which was carried out by the Sifo polling firm at the request of Sveriges Television (SVT), said they were afraid of being spied on by the Swedish state or foreign powers.
"I thought more would be afraid, considering the current debate," chief Sifo polling analyst Toivo Sjören told SVT.
As the polling firm hasn't ever looked at Swedes' fears about internet surveillance, it's hard to assess how the figure may have been changed in light of reports about NSA's data gathering techniques.
The results, based on interviews with 1,109 Swedes, came on the same day that members of the parliamentary Committee on Defence (Försvarsutskottet) questioned officials at the Swedish Defence Radio Establishment (Försvarets radioanstalt, FRA) about the agency's signals intelligence operations.
The MPs spent roughly two hours at the agency on Thursday probing high-ranking officials over the agency's adherence to current laws governing data collection for intelligence purposes as well as whether the agency monitors Swedish politicians.
Allan Widman of the Liberal Party (Folkpartiet) said he left the meetings with a "crystal clear" understanding that FRA followed rules dictating that any intelligence collection in Sweden can only occur in the context of foreign relations.
He emphasized the FRA is a "relatively small" agency compared to those of other powers.
"The hard part probably isn't collecting information but rather analyzing it and extracting something usable from it," he told the TT news agency.
He added that he didn't get any indications of the extent of the information exchange that occurs between FRA and its counterpart agencies in other countries, emphasizing that it is the government that ultimately decides "which democratic states Sweden has defence intelligence cooperation with".
At the weekend, media reports citing leaks by Snowden singled out Sweden as one of the main partner countries of the British signals intelligence agency GCHQ.
The reports came in the wake of claims made earlier in the year by British investigative journalist Duncan Campbell that Sweden collaborated with the United States in passing laws in 2008 that gave FRA the power to monitor cable-bound communications traffic.
"When you put together the pieces of the puzzle it becomes clear that Sweden worked together with the US and the UK in order to create new laws for mass surveillance online," Campbell told the Dagens Nyheter (DN) newspaper at the time.
While Widman expressed his satisfaction with Thursday's meetings at FRA, politicians on the left expressed lingering concerns about the agency's capacity to gather and store information about Swedish citizens.
While laws prohibit monitoring communication between people in Sweden, data obtained by FRA can be retained for a limited amount of time in cases when the agency needs to clear up uncertainty about how communications were carried out.
"They say they don't store that much, that they get rid of everything required by the law," Green Party MP Peter Råberg told TT, cautioning however that FRA nevertheless "can retain quite a lot".
"My previous concerns remain."
Some experts have also expressed alarm over Swedes' apparent lack of concern about the extent to which their online activities can be monitored.
"The fact that so many aren't at all uneasy about surveillance is troubling in and of itself," internet researcher Marcin de Kaminski from Lund university wrote in an opinion piece published by SVT Debatt.
Kaminski argued that part of Swedes' blasé attitude likely stems from a lack of awareness and understanding of the issue among the general public.
"We haven't succeeded in making the whole mess comprehensible," he wrote.
"The seriousness of the issue hasn't come through, despite the fact that our society's future in essence rests on us being able to trust the technical systems on which we all depend. This frightens me."