By Barbara Goldberg and Joseph Ax

NEW YORK (Reuters) - Airports in major U.S. cities were on high alert on Tuesday, with police out in force after at least 30 people were killed in suicide bombings on a Brussels airport and subway, though officials said there was no specific threat to the United States.

U.S. President Barack Obama and Democratic presidential election contender Hillary Clinton vowed to do more to take on militants, while Republican presidential front-runner Donald Trump called for tighter border security and suggested U.S. intelligence services could use torture to head off future attacks.

The Obama administration was expected to tighten security at U.S. airports following the Brussels airport attack, which occurred in a public hall outside of the security check area.

U.S. Representative Adam Schiff of California, the ranking Democrat on the House intelligence committee, said he was concerned that there was a risk of copy cat attacks and that airport security was still a concern despite changes in recent years.

"Overall though there's a lot more work we still need to do at our airports," Schiff told MSNBC.

Islamic State, a militant group that has gained control of large areas of Iraq and Syria and has sympathizers and supporters around the world, claimed responsibility. Amaq, a news agency affiliated to the group, said suicide bombers strapped into explosive belts had staged the attacks on the airport and a rush-hour metro train in the Belgian capital.

Delta Air Lines Inc, United Continental Holdings Inc and American Airlines Group Inc reported that they had canceled or rerouted flights as a result of the attack.

Large numbers of uniformed police officers, some in tactical gear as well as National Guard members in fatigues and carrying long weapons, were on patrol at New York's John F. Kennedy International Airport.

One guard member was overheard telling a colleague "we have to keep an eye out for bags" after reports that many of the wounded at the Brussels airport had severe leg injuries, according to officials, a pattern that suggests an explosion at ground-level, possibly from a bag.

Some travelers in the United States said they hoped airports would further tighten security following the Brussels attack.

"Perhaps it should take place sooner, before you get through security. I find it reassuring," said Mary Ray, 71, a retired government trainer flying home to Manchester, England, from New York after a Caribbean cruise with her husband, Malcolm.

Ray said she is happy to remove her shoes or have her hands swabbed as she passes through airport security: "I think it's a deterrent."

Three Mormon missionaries from the United States were injured in the airport blasts, the Church of Jesus Christ of Latter-Day Saints said. A U.S. service member and his family were hurt, Fox news reported, but gave no details.

European and U.S. airports have extensive security in place to prevent weapons from being smuggled onto aircraft, but the attackers exploited an area not subject to screening.

'SCOURGE OF TERRORISM'

Obama addressed the attacks briefly in a speech in Havana on his historic first visit to Cuba, vowing to support Belgium as it seeks out those responsible.

"This is yet another reminder that the world must unite. We must be together regardless of nationality or race or faith in fighting against the scourge of terrorism," Obama said. "We can and we will defeat those who threaten the safety and security of people all around the world."

Islamic State was blamed for killing 130 people in Paris last November. Then in December, a married couple inspired by Islamic State shot dead 14 people in San Bernardino, California.

The attacks in Belgium drew immediate response from candidates seeking their party's nomination to run for the White House in the Nov. 8 election.

Former U.S. Secretary of State Clinton vowed to strengthen her drive to "defeat terrorism and radical jihadism." She said on CNN that the United States must do more to coordinate intelligence with Europe.

Billionaire Trump told NBC's "Today" program: "If they could expand the laws, I would do a lot more than waterboarding. You have to get the information from these people."

He was referring to the practice of pouring water over someone's face to simulate drowning as an interrogation tactic. Obama banned its use by U.S. interrogators after taking office in 2009.

Officials in cities including New York, Washington, Boston and Miami said they were aware of no specific threats targeting them following the Brussels attack.

While the attack immediately sparked discussion of further strengthening airport security, some pointed out the inherent difficulty of securing spaces that offer broad public access.

"There are limits to exactly how exhaustive those perimeters can become," U.S. Secretary of State John Kerry said in an interview with Telemundo. "So people need to be vigilant, everybody needs to take precautions. I think it underscores to everyone the importance of people uniting."

As she rushed to meet clients arriving at New York's JFK airport, 31-year-old Shannon Freyer worried that adding further layers of security at airports, which have already imposed extensive restrictions since the Sept. 11, 2001 hijacked plane attacks, would do little to make people safer.

"It's just more time involved," Freyer said. "They started making us take off our shoes years ago and they still haven't stopped a thing."

(Additional reporting by Mark Hosenball, Ian Simpson and Susan Heavey in Washington and Suzannah Gonzales in Chicago; Writing by Scott Malone; Editing by Bill Trott and Grant McCool)

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