JUDY WOODRUFF: A massive investigation of the terrorist attacks in Paris was in full swing across France and Belgium today. The death toll stood at 129, with some 350 wounded in Friday's coordinated assault, now claimed by the Islamic State group.

Hari Sreenivasan is in Paris, where he begins our coverage.

HARI SREENIVASAN: Thanks, Judy.

It was a day of remembrance and resolve. The victims of the massacre were remembered, memorialized once again, but France also began a forceful response against the Islamic State.

Silence fell across Paris at noon today and across much of Europe, as millions remembered victims of Friday's attacks.

The French president remembered victims from 19 countries at a courtyard at the Sorbonne.

A short time later, Francois Hollande went before Parliament to declare that France is at war.

PRESIDENT FRANCOIS HOLLANDE, French President (through interpreter): The French people are ardent, valiant, courageous. They don't give up. They stand up when each of their children is put in the ground. Those who wanted to murder them by deliberately striking innocent people are cowards who fired on an unarmed crowd.

HARI SREENIVASAN: Across the country, authorities conducted a sweeping dragnet of people they suspect of militant ties and found caches of weapons, including rocket launchers.

BERNARD CAZENEUVE, French Interior Minister (through interpreter): Throughout France overnight, police and armed police, with the help of the central and regional branches of our intelligence services, carried out 168 raids in the homes of people under suspicion.

HARI SREENIVASAN: At the same time, a fuller picture of those suspected in the plot came into focus, including Abdelhamid Abaaoud, the alleged mastermind. The Belgian-born militant is seen here in the Islamic State propaganda magazine, but is now believed to be in Syria.

In all, at least eight men mounted the Friday attacks at the Bataclan theater, at the Stade de France and two restaurants. At least one attacker carried a possibly fake Syrian passport and may have entered Europe through Greece, with the flood of refugees. Most of the others are believed to be French-born Muslims who may have traveled to Syria. Seven died in the attack, while the eighth, 26-year-old Salah Abdeslam, is thought to have escaped to Brussels.

With that in mind, President Hollande announced drastically stepped-up security measures, including broader police powers and border controls. It's the third day of mourning for the city of Paris. Government buildings, museums even the Eiffel Tower are closed. People around the city are now thinking about what to do next.

WOMAN: Closing down the borders won't change anything. You know, there's always — we always have refugees coming in the country, or in any other countries.

HARI SREENIVASAN: We sat down with 49-year old Emmanuel Pohrel outside a cafe as trucks made their morning deliveries.

WOMAN: If you think of security all the time, you just become crazy and paranoid.

HARI SREENIVASAN: Pohrel is also concerned about the increasing scrutiny refugees and immigrants will face.

WOMAN: I don't think those people who come in are terrorists. They're just going away from a country where there's a war.

HARI SREENIVASAN: This is a tension playing out across the city and perhaps the country, even as young and old visit the sites of Friday night's rampage to pay their respects, to grieve.

While we spoke to Brigitte Fraisse outside the Cambodian restaurant that was struck Friday night, the place her daughter introduced her to, another woman walking by.

That woman said, close the borders, while Ms. Fraisse said open the borders. In a different neighborhood, we met a 63-year-old realtor named Thierry Preguica.

THIERRY PREGUICA, France (through interpreter): I think the Western world crumbles little by little. I think we're facing a problem we don't control any longer.

HARI SREENIVASAN: Preguica is on the side of increased security at the borders.

THIERRY PREGUICA (through interpreter): Unfortunately, today, we need to strike hard, because we are facing a very determined, blind enemy, who has no logic, or, rather, has a barbaric logic. So, today, our established rules, they are a bit dated, I think.

PRESIDENT BARACK OBAMA: We have always understood this would be a long-term campaign. There will be setbacks and there will be successes. The terrible events in Paris were obviously a terrible and sickening setback.

HARI SREENIVASAN: President Obama, at the G20 in Turkey, acknowledged Islamic State had struck a major blow, but he defended U.S. strategy against repeated questions about whether he's underestimated the militants.

PRESIDENT BARACK OBAMA: We have the right strategy, and we're going to see it through. There will be an intensification of the strategy that we put forward, but the strategy that we are putting forward is the strategy that ultimately is going to work.

We haven't underestimated our abilities. This is precisely why we're in Iraq as we speak and why we're operating in Syria as we speak. And it's precisely why we have mobilized 65 countries to go after ISIL. There has been an acute awareness on the part of my administration from the start that it is possible for an organization like ISIL that has such a twisted ideology and has shown such extraordinary brutality and complete disregard for innocent lives, that they would have the capabilities to potentially strike in the West.

HARI SREENIVASAN: In a video released today, an Iraqi fighter with ISIL threatened more strikes against the countries in the coalition, and inside the U.S.

AL-KARAR AL-IRAQI, ISIS (through interpreter): We say to the states that take part in the crusader campaign that, by God, you will have a day, God willing, like France's. And by God, as we struck France in the center of its home in Paris, then we swear that we will strike America at its center in Washington.

HARI SREENIVASAN: Aware of the risk, U.S. authorities have increased security at airports and in major cities. But there are Republicans in Congress and on the campaign trail who say that the U.S. must do more.

SEN. LINDSEY GRAHAM, Republican Presidential Candidate: There is no substitute for a ground component in this war. The region would supply the bulk of the forces. We would have to be part of it. At the end of the day, we can destroy ISIL. We must destroy ISIL. And the average American gets it. I want to fight them in their backyard, so we don't fight them in our backyard. Those are your two choices.

HARI SREENIVASAN: The president pushed back against suggestions that thousands of American troops should be sent to the Middle East.

PRESIDENT BARACK OBAMA: We play into the ISIL narrative when we act as if they're a state and we use routine military tactics that are designed to fight a state that is attacking another state. That's not what's going on here.

These are killers with fantasies of glory who are very savvy when it comes to social media and are able to infiltrate the minds of not just Iraqis or Syrians, but disaffected individuals around the world. And when they activate those individuals, those individuals can do a lot of damage.

HARI SREENIVASAN: Paris was the latest demonstration of that damage, indicating a possible strategic shift outside the group's self-proclaimed caliphate, including the suspected bombing of a Russian airliner over Egypt's Sinai Peninsula that killed more than 200, suicide bombings in Beirut suburbs last week that killed more than 40, and attacks in Turkey and Tunisia that killed nearly 200 people.

Based on intelligence supplied by the U.S., France is already responding to Friday's attacks with intense new airstrikes in Syria, targeting Raqqa, the city the Islamic State uses as its capital.

And tonight in Paris, after standing darkened for two nights, the Eiffel Tower is again lit, now in the blue, white and red of the French tricolor flag, its spotlight shining across a tense and grieving city.