The US institute's survey across European countries shows growing concern about the historic influx of more than one million asylum seekers last year and about the integration of minority groups, Muslims in particular.
In eight of the ten countries surveyed, representing 80 percent of the European population, at least half of the public believe that "incoming refugees increase the likelihood of terrorism in their country", the survey said.
In Germany - the largest EU economy, which last year took in the biggest number of migrants and refugees - 61 percent shared this concern, while 60 percent of Italians and 52 percent of British voiced the same fears.
Paradoxically, in France, a country hard hit by jihadist attacks in 2015, only 46 percent thought the danger of an attack had increased.
The view was held most strongly, by 76 percent of respondents, in Hungary and by 71 percent in Poland - both countries which have received proportionately few migrants as their governments have adopted a tough stance toward refugees.
In general, the Pew Center found that "the refugee crisis and the threat of terrorism are very much related to one another in the minds of many Europeans".
"The recent surge of refugees into Europe has featured prominently in the anti-immigrant rhetoric of right-wing parties across the continent and in the heated debate over the UK's decision to exit the European Union," it pointed out.
The study found that perceptions of refugees are influenced in part by negative attitudes toward Muslims already living in Europe.
"In Hungary, Italy, Poland and Greece, more than six-in-ten say they have an unfavourable opinion of the Muslims in their country - an opinion shared by at least one-in-four in each nation polled," it said.
The study also found that majorities in seven of ten countries saw the arrival of refugees as "a burden on our country because they take our jobs and social benefits".
The proportion who held this view reached 82 percent in Hungary, 75 percent in Poland, 72 percent in Greece, 65 percent in Italy and 53 percent in France.
In top refugee destinations Germany and Sweden, however, majorities did not share this fear and believed refugees make their nations stronger because of their work and talents.
Pew said the survey was conducted with 11,494 respondents between April 4th and May 12th.