WASHINGTON, Aug 31 (Reuters) - The United States is having more success fighting terrorism under President Barack Obama partly because of his "radically different" approach to foreign policy, National security adviser Jim Jones said on Monday.

In an interview with ABC News, Jones said Obama's efforts to reach out to world leaders and improve relations with law enforcement agencies had made it easier to track and kill terrorists than during the Bush administration.

"We have better human intelligence. We know where the terrorists are moving," Jones told ABC.

"Because of the dialogue and the tone of the dialogue between us and our friends and allies ... the trend line against terrorism is positive," he added.

Jones spoke a day after former Vice President Dick Cheney said he has serious doubts about the extent to which Obama understood and is prepared to do what is needed to defend the United States from attack.

Cheney has been a persistent critic of Obama's approach to foreign policy and security issues, accusing the U.S. leader of putting in place policies that could encourage anti-U.S. militants to attack the United States.

While noting that he was not keeping tallies of enemy combatants killed and captured under Obama and Bush, Jones said the numbers were going up as a result of good intelligence.

"We are seeing results that indicate more captures, more deaths of radical leaders and a kind of a global coming-together by the fact that this is a threat to not only the United States but to the world at-large," he said.

He also dismissed Cheney's assertion that the Bush administration's counterterrorism policies worked because there had not been any terrorist attacks on U.S. soil after September 11, 2001.

"It's very easy to leave office and say, 'Well, no other disaster happened on the size and scope of 9/11, so we did our job well.' Well, maybe they did, maybe they didn't."

Jones did not, however, counter Cheney's argument that Attorney General Eric Holder's decision to investigate suspected CIA prisoner abuses could have a chilling effect on the work of the intelligence agency.

"I think it is something we have to address," Jones said. "I think anybody who works in a law enforcement agency ... have to know clearly what the rules are." (editing by Paul Simao)