By Guy Faulconbridge and Sarah Young

LONDON (Reuters) - World leaders responded to deadly attacks in Paris with defiant pledges of solidarity and Europe tightened security after Islamic State said it was behind an assault by gunmen and bombers that left at least 129 dead in the French capital.

From Barack Obama to Vladimir Putin and across Europe and the Middle East, leaders expressed their condolences to French President Francois Hollande who said the attacks amounted to an act of war against France.

After the worst bloodshed in France since the end of World War Two, European neighbors including Britain, Belgium, Switzerland, Germany and Italy increased security. France temporarily imposed border controls.

British Prime Minister David Cameron used French to express his solidarity after calling Hollande.

"Shocked, but resolute. In sorrow, but unbowed. My message to the French people is simple: Nous sommes solidaires avec vous. Nous sommes tous ensemble. We stand with you. United," Cameron said.

London monuments including the London Eye and Tower Bridge were lit up in the red, white and blue of the French tricolor, as were Sydney's Opera House, the Taipei 101 skyscraper in Taiwan, the Senate building in Mexico City, One World Trade Center in New York and several other global landmarks.

The deadliest attack on Europe since the 2004 Madrid bombings laid bare Islamic State's capability to strike at the heart of Europe and the difficulty of monitoring the movements of militants intent on killing.

It also triggered a debate on Europe's refugee policies and the failures of Western policy in Syria.

DEATH IN PARIS

"This is an attack not just on Paris, it’s an attack not just on the people of France, but this is an attack on all of humanity and the universal values that we share," Obama said.

German Chancellor Angela Merkel echoed Obama, saying "our free life is stronger than terror."

New York, Los Angeles, Boston and other cities in the United States bolstered security, but law enforcement officials said the beefed-up police presence was precautionary rather than a response to any specific threats.

Story continues

On Saturday in New York, hundreds of people including Mayor Bill de Blasio gathered for a vigil at Washington Square Park in Greenwich Village. The park is known for a landmark arch modeled after the Arc de Triomphe in Paris. Some of the crowd held signs of a peace symbol with the Eiffel Tower at its center. At dusk, the city was planning to light the arch in the blue, white and red of the French flag.

Roya Hegdahl, a 21-year-old Columbia University student from Seattle, stood at the vigil with a French flag draped around herself and her French roommate.

"I have a lot of anxiety about how the world will react to the situation because in these moments it's easy to act out of fear and anger, which often doesn't lead to the best decision and policy making," Hegdahl said.

At Times Squares, the New York Police Department marshaled about 200 officers and dozens of vehicles at Times Square in a show of force reminiscent of exercises the NYPD staged regularly in the months after the Sept. 11, 2001, attacks on the World Trade Center.

In Los Angeles, the second-largest U.S. city, police said they stepped up patrols at concerts and other places with large crowds.

Western security sources said the attack on Paris was one of the "nightmare" scenarios for police forces: several well planned attacks with advanced weaponry on unarmed civilian revelers across a densely populated capital.

The attacks included explosions outside a stadium where the French and German men's national soccer teams were playing an international match.

In response, the National Football League said it would increase security and beef up law enforcement presence at stadiums this weekend as a precaution, even though there was no known threats to any of the venues.

Islamic State militants said the attack was designed "to teach France, and all nations following its path, that they will remain at the top of Islamic State’s list of targets".

Hollande said the attack was planned outside France but carried out with internal help.

Western security sources said the porous nature of Europe's internal borders - hailed as one of the major achievements of European integration - also allowed freer movement of advanced weaponry and potential attackers, including those who have traveled to Syria, across Europe.

EUROPE'S BORDERS

Dutch Prime Minister Mark Rutte said the Netherlands would tighten security at its borders and airports, and said the Dutch were "at war" with Islamic State.

Belgium imposed additional frontier controls on road, rail and air arrivals from France and Belgian Prime Minister Charles Michel asked Belgians on Saturday not to travel to Paris unless necessary.

“Border control is absolutely critical,” said Anthony Glees, director of the Centre for Security and Intelligence Studies at the University of Buckingham.

“They can reinstate border controls so they know who is in their country, they know who leaves their country and they know where they’ve been if they leave their country.”

European Union leaders said that such attacks could not divide Europe.

But in a sign of potential divisions ahead, Poland's European affairs minister designate said after the attacks in Paris, Warsaw would not be able to accept migrants under European Union quotas.

In September, Poland backed a European Union plan to share out 120,000 refugees, many of them fleeing the war in Syria, across the 28-nation bloc.

The attacks have also sparked a debate in Germany on Chancellor Angela Merkel's refugee policy and how to get a better overview of the people entering the country.

(Additional reporting by Alastair Macdonald in Brussels, Mark Hosenball in Washington, Lena Masri and Roselle Chen in New York and Alex Dobuzinskis in Los Angeles,; Editing by Sonya Hepinstall, Bernard Orr and David Gregorio)