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.

The overall share saying any kind of attack is likely has risen 10 points since late last year.

That finding came from a poll conducted between the terror attacks in Paris in November and the shooting attack in San Bernardino, California, in December.

The increase since then is sharpest among Democrats, 60% of whom now say such an attack is likely, up from 47% in the late-2015 poll.

The equivalent percentage has climbed 9 points among independents to 72% and 8 points among Republicans to 84%.

Despite increased concerns about a looming attack, fears of becoming a terror victim have dampened compared with after the San Bernardino shootings, 41% are at least somewhat worried that they or a family member will become a victim, down from the 45% who said so in December.

At the same time, President Barack Obama’s approval ratings for handling terrorism and ISIS have inched upward since December, but they remain largely negative.

His approval rating is higher on handling terrorism (42%) than it is on dealing with ISIS (38%), with 60% disapproving of his handling of ISIS and 56% disapproval for his handling of terrorism.

The CNN/ORC Poll was conducted by telephone June 16-19 among a random national sample of 1,001 adults.

Results for the full sample have a margin of sampling error of plus or minus 3 percentage points.