The mushrooming of small-scale terror attacks in Europe has allowed Islamic State and its adherents to keep people here on edge without having to train and equip teams to pull off highly sophisticated operations.

Indeed, some U.S. officials say they believe some of the simpler attacks on softer targets of the type seen recently will prove to have been directed by Islamic State, not just inspired by the group.

“We know there is a command and control structure behind some of these attacks,” said a U.S. official. “Islamic State has filled up the pipeline with militants in Europe.”

According to U.S. officials the smaller attacks may be designed to overwhelm law-enforcement and intelligence services—helping operatives planning a bigger attack to move around undetected.

U.S. military officials have insisted for months that the greater frequency of attacks in Europe is a response to the pressure Islamic State is feeling in Syria and Iraq as it has lost territory in its self-declared caliphate.

Other U.S. officials have dismissed that theory, however, noting that Islamic State’s plotting predates its recent losses. These officials said the frequency and scale of the recent attacks reflects Islamic State adapting to new obstacles.

Bruce Hoffman, a terrorism expert and professor at Georgetown University, said Islamic State has been working for years to plant the seeds for the kind of small-scale attacks Europe is now seeing.

“They put in place an infrastructure across Europe to facilitate the movement of people to and from Iraq and Syria, but also to provide a bedrock of both inspirational and operational support for terror attacks,” he said.

One of the attacks, the suicide bombing in Germany that injured 12 people, appears to have been directed by Islamic State, according to U.S. and European officials. Others have less clear connections, officials said.

France’s top prosecutor said last week that the man behind the July 14 attack in Nice had conspired with others for many months. Investigators were examining whether the men had connections to Islamic State or other extremist groups,

That attack killed 84 people. But attacks since then have had far fewer casualties.

Unlike the Paris and Brussels attacks, carried out by a trained core of militants with carefully constructed plans, recent ones have used relatively unsophisticated means, including knives and even a rented truck.

“These are amateurs, they aren’t the hardened jihadists,” said Rik Coolsaet, a professor at Ghent University and expert on jihadist terrorism. “While they can be lethal, with high body counts as in Nice, most often they are not.”

In any case, U.S. and European officials say Islamic State hasn’t abandoned its desire to carry out large-scale terrorism.

Devin Nunes, the chairman of the U.S. House intelligence committee, said “constant, even daily, terror attacks” in Europe could become the norm.

“The jihadist threat is not going away any time soon—in fact, it’s likely to grow even more acute,” Mr. Nunes said. “The bottom line is that radical Islam has declared war on the West.”

According to Western officials and Syrian activists, as the border between Syria and Turkey and between Turkey and Greece has tightened, some would-be militants have altered their plans.

Adel Kermiche, a 19-year-old Frenchman who killed a priest in Normandy on Tuesday, had intended to fight for Islamic State in Syria, according to French and U.S. officials. He was ordered to wear a monitoring bracelet by a French judge after he twice tried and failed to slip into Syria last year.

“They are striking here because they can’t get to where they want to go,” said a U.S. official in Europe.