MOSCOW - A suicide bomber carrying a suitcase walked into Moscow's busiest airport and set off a huge explosion Monday, killing 35 people and wounding 180.

The international arrivals terminal at Domodedovo Airport was engulfed by smoke and splattered with body parts after the mid-afternoon terror attack sprayed shrapnel, screws and ball bearings at passengers and workers. Hundreds of people were in the loosely guarded area at the time.

President Dmitry Medvedev immediately ordered authorities to beef up security at Moscow's two other commercial airports and other key transport facilities. He also canceled plans to fly out Tuesday to Davos, Switzerland, where he was going to promote Russia as a safe, profitable investment haven to world business leaders.

"Attempts were being made to identify" the suspected male suicide bomber, Investigative Committee spokesman Vladimir Markin said, adding that the attacker appeared to have been wearing the explosives in a belt.

The Interfax news agency said the head of the suspected bomber had been found.

No one immediately claimed responsibility for the explosion, which occurred at 4:32 p.m. (1332GMT). But Chechen militants have claimed responsibility for previous terror attacks in Moscow, including a double suicide bombing on the subway in March 2010 that killed 40 people and wounded more than 100.

The latest attack on the Russian capital also called into question Russia's ability to safely host major international sports events like the 2014 Winter Olympics in Sochi and the 2018 World Cup. It was the second time in seven years that terrorists had hit the Domodedovo Airport: In 2004, suicide bombers penetrated the lax security there, killing 90 people as they blew up two planes.

Large-scale battles in Chechnya ended years ago, following two devastating wars between Russia and the republic's separatists, but Islamic militants have continued to carry out suicide bombings and other attacks. Most of the attacks have been in Chechnya and other predominantly Muslim provinces in the southern Caucasus region, but some have targeted Moscow, including its subways, buses and trains.

In Washington, President Barack Obama condemned the "outrageous act of terrorism" and offered any assistance Russia might want. Those comments were echoed by British Prime Minister David Cameron, who spoke with Medvedev and assured him of his complete support.

The Emergencies Ministry said 35 people were killed, 86 hospitalized with injuries and 94 were given medical treatment. Two Britons were among the dead, Markin said.

Amateur video posted on YouTube showed a pile of bodies on the airport floor, and other bodies scattered around. Luggage lay strewn across the ground and several small fires burned. A dazed man in a suit pushed a baggage cart through the carnage.

Another man in blood-soaked clothes said he was just a few yards (meters) away from the explosion and saw a man who may have been the suicide bomber.

"I saw the suitcase, the suitcase was on fire," said Artyom Zhilenkov, a 35-year-old driver. "So either the man blew up something, or something went off on the man's body, or the suitcase went off."

Zhilenkov said he thought he himself had been injured but doctors said he was just coated in other victims' blood.

"The guy standing next to me was torn to pieces," he said.

Car rental agent Alexei Spiridonov, 25, was at his desk when the blast struck about 100 yards (meters) away.

"The explosion was so strong that it threw me against the wall," he said outside the airport. "People were panicking, rushing out of the hall or looking for their relatives. There were people just lying in blood."

Yelena Zatserkovnaya, a Lufthansa official, said airport workers used baggage trolleys to cart out the injured.

"There was lots of blood, severed legs flying around," she said.

Prime Minister Vladimir Putin ordered the health minister to make sure all victims received immediate attention, instructing her to send her deputies to clinics to check on treatment.

Russians still look to the tough-talking Putin as the leader they trust to guarantee their security, and Monday's attack was likely to strengthen the position of the security forces that form part of his base.

Sergei Lavochkin, who was waiting for a friend to arrive from Cuba, said passengers sprinted out of the terminal after the blast and emergency teams carried out those unable to walk.

"I heard a loud bang, saw plastic panels falling down from the ceiling and heard people screaming. Then people started running away," Lavochkin told Rossiya 24 television.

Aviation security experts have been warning since the September 11, 2001, terror attacks that the crowds at many airports present tempting targets to suicide bombers. Arrivals halls are usually open to anyone.

"Airports are by their nature crowded places, with meeters, greeters, commercial businesses, and so on," said Philip Baum, the editor of Aviation Security International, a London-based publication dedicated to security issues.

Domodedovo was briefly closed to air traffic immediately after the blast, but soon reopened. Hours later, passengers arriving for their flights lined up outside waiting to pass through metal detectors that had been installed at all entrances.

Built in 1964, Domodedovo is located 26 miles (42 kilometers) southeast of Moscow and is the largest of the three major airports that serve the Russian capital, handling over 22 million people last year. It is generally regarded as Moscow's most up-to-date airport, but its security procedures have been called into question.

In 2004, two suicide bombers were able to board planes at Domodedovo by buying tickets illegally from airport personnel. The female bombers blew themselves up in mid-air, killing all 90 people aboard the two flights.

Some 77 airlines now offer regular flights to Domodedovo, serving 241 international and national routes, according to airport's website.

The airport insists that security is one of its top priorities, claiming on its website that its "cutting-edge operations technology guarantees the safety of passengers' and guests' lives."

NATO Secretary-General Anders Fogh Rasmussen said he was "deeply disturbed" by the terror attack.

"I strongly condemn it," he said on Twitter. "NATO and Russia stand together in the fight against terrorism."

It was not clear late Monday if Medvedev would still give the opening address Wednesday at the World Economic Forum in Davos.

FIFA President Sepp Blatter was in St. Petersburg over the weekend to formally award Russia the 2018 World Cup. Prior to the signing, Blatter told Putin that he was certain FIFA had made the right choice.