BEIRUT, Lebanon — In a matter of hours and on three different continents, militants carried out attacks on Friday that killed scores of civilians, horrified populations and raised thorny questions about the evolving nature of international terrorism and what can be done to fight it.

On the surface, the attacks appeared to be linked only by timing.

In France, a man stormed an American-owned chemical plant, decapitated one person and apparently tried to blow up the facility. In Tunisia, a gunman drew an assault rifle from a beach umbrella and killed at least 38 people at a seaside resort. And in Kuwait, a suicide bomber blew himself up inside a mosque during communal prayers, killing at least 25 Shiite worshipers.

The Islamic State group claimed responsibility for the attacks in Tunisia and Kuwait, according to statements on Twitter. But it almost did not matter for terrorism’s global implications whether the three attacks were coordinated. Each in a different way underlined the difficulties of anticipating threats and protecting civilians from small-scale terrorist actions, whether in a mosque, at work or at the beach.

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The attacks occurred at a time of fast evolution for the world’s most dangerous terrorist organizations, which continue to find ways to strike and spread their ideology despite more than a decade of costly efforts by the United States and others to kill their leaders and deny them sanctuary.

The United States has killed leaders of Al Qaeda in Afghanistan, Yemen and elsewhere, but the group has maintained a string of branches and melded itself into local insurgencies. The Islamic State, also known as ISIS or ISIL, has worked on two levels, seeking to build its self-declared caliphate on captured territory in Iraq and Syria while inciting attacks abroad.

Fueling that expansion are civil wars and the collapse of state structures in Arab countries from Libya to Yemen that have opened up ungoverned spaces where jihadists thrive, while social media has given extremists a global megaphone to spread their message.

While officials in the three countries investigated the attacks, many noted that leaders of the Islamic State have repeatedly called for sympathizers to kill and sow mayhem at home.

Earlier this week, the spokesman for the Islamic State, Abu Mohammed al-Adnani, greeted the group’s followers for Ramadan, telling them that acts during the Muslim holy month earned greater rewards in heaven.

“Muslims, embark and hasten toward jihad,” Mr. Adnani said in an audio message. “O mujahedeen everywhere, rush and go to make Ramadan a month of disasters for the infidels.”

FRANCE

KUWAIT

TUNISIA

About three hours

after first attack

First attack

About two hours

after first attack

Imam Sadiq

Mosque

Air Products

Factory

Imperial

Marhaba

Hotel

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By The New York Times

The attacks targeted each country in a particularly sensitive spot.

Tunisia, widely hailed as the sole success of the Arab Spring uprisings that began more than four years ago, suffered a sharp blow to its tourism sector, a pillar of the local economy.

The bombing in Kuwait followed the pattern of similar attacks on Shiite mosques in Saudi Arabia and was aimed at sowing sectarian divisions in a country where Sunnis and Shiites serve together in top government bodies and open friction between the sects is uncommon.

The motivation behind the attack in France was less clear, although the beheading suggested that the perpetrator had at least been inspired by the Islamic State, which frequently propagandizes similar killings in the territories it occupies.

And because the day’s events appeared to bear some of the infamous hallmarks of the Islamic State and its supporters, some analysts speculated that the attacks had been timed to mark the first anniversary of its declaration of a caliphate. Even if that is not the case, the SITE intelligence Group, which tracks extremist propaganda, said the attacks inspired “celebration from Twitter accounts of Jihadi fighters and supporters of the Islamic State.”

Lina Khatib, director of the Carnegie Middle East Center in Beirut, said “We have entered a new jihadist era,” adding that the Islamic State had used its international brand to establish sleeper cells abroad, whose actions were meant to advance its efforts to build a state

“Everything in the end serves the purpose of strengthening the project of the Islamic State,” she said.

United States intelligence and counterterrorism officials were scrambling Friday to assess the connections, if any, between the attacks in France, Kuwait and Tunisia. Officials said that if the assessment found that the attacks were linked, officials would seek to determine whether the Islamic State had actively directed, coordinated or inspired them.

Col. Steve Warren, a Pentagon spokesman, condemned the attacks, which he called “heinous.” But there was no word yet on whether they were coordinated, he said. “We just don’t know yet.”

In claiming the Kuwait attack, the Islamic State called the suicide bomber “one of the knights of the Sunni people” and lauded him for killing Shiites, who are considered apostates in the group’s hard interpretation of Islam.

The assault resembled others launched by the Islamic State recently on Shiite mosques in neighboring Saudi Arabia, prompting many to believe that the militant group is seeking to set off a sectarian war between Sunnis and Shiites.

“Ever since I heard about Qatif and the Shiite mosques there, I just had this feeling that we were next,” said Bodour Behbehani, a Shiite graduate student in Kuwait City, recalling a mosque bombing last month near Qatif, a city in Saudi Arabia.

The American war on terrorism has taken many forms over the years. But the spread of such small-scale attacks highlighted what even American officials have called a failure to win the ideological — or information — war that feeds militancy and inspires recruits.

The challenge, analysts and government officials say, is to reorient a strategy centered on combat to one that challenges extremist groups on all fronts simultaneously: political, social, ideological and religious. A primary aim, they say, should be to win the information war and undermine the appeal of radical Islamist ideologies.

Such terrorist attacks have shattered the assumption that the Islamic State can be confined to territories it controls in the Middle East, said Bruce Hoffman, director of the Center for Security Studies at Georgetown University. Although Western governments can work to monitor those who might be plotting attacks, this will not solve their root cause.

“Chasing individuals is probably a fool’s errand given the geographically disparate nature of the threat,” Dr. Hoffman said. “There comes a point where you have to tackle the organization behind it.”

And monitoring has limits. The authorities in Tunisia said the gunman there was a young Tunisian with no prior police record. The authorities in France said that the attacker arrested there had connections to radical Islamists but that surveillance of him stopped in 2008.

The Kuwaiti authorities did not identify the attacker in their country.