Story highlights A new CNN/ORC poll finds 71% of Americans say further acts of terrorism are very or somewhat likely

Concerns about a terror attack in the U.S. haven't been that high since March 2003

Washington (CNN) Americans are more likely to think terrorist attacks in the U.S. are imminent now than at any point since 2003, according to a CNN/ORC Poll conducted after a shooting in Orlando that ranks as the worst terrorist attack on U.S. soil since 9/11.

Overall, 71% say further acts of terrorism are very or somewhat likely in the United States over the next several weeks.

Concerns about a terror attack in the U.S. haven't been that high since March 2003, in the days after the U.S. began its war with Iraq. Nearly one-quarter of Americans, 24%, consider an attack "very likely," and except for a survey conducted just after Osama bin Laden's death in May 2011, that's the highest share to say so since November 2001.

Americans' concerns about domestic terror are more focused on so-called "lone-wolf" attacks carried out by individuals who say they have been inspired by a terrorist group rather than attacks organized and supported by terrorist groups themselves.

Nearly three-quarters of Americans say individual attacks are a greater threat than attacks organized by terrorist groups, just 23% see organized attacks as the bigger threat. Although majorities across party lines agree that lone-wolf attacks are a bigger danger than organized ones, Republicans are a bit less likely to say individual attacks are the larger threat. Among Republicans, 68% see individual attacks as a bigger threat vs. 75% each among Democrats and independents.

Read More