“Now, my job is to communicate the fact that the United States has a stake in the well-being of the Muslim world, that the language we use has to be a language of respect,” he told the Saudi-owned station. “I have Muslim members of my family. I have lived in Muslim countries.”

Mr Obama spent four years of his childhood in Indonesia, which is widely tipped to be the first majority-Muslim country he will visit within his first 100 days in office.

He pledged his strong backing for the peace brokering efforts of George Mitchell, the former Senator, whom he appointed last week as his special envoy for the Israel and Palestine. Mr Mitchell is expected to visit the region within the next few days.

Mr Obama implicitly conceded in the interview that terms such as “war on terror” had proved counter-productive over the last seven years. “The language we use matters,” he said. “We cannot paint with a broad brush a faith as a consequence of the violence that is done in that faith’s name. I cannot respect terrorist organizations that would kill innocent civilians and we will hunt them down. But to the broader Muslim world what we are going to be offering is a hand of friendship.”

Just five days into office, Mr Obama has issued several executive orders declaring an end to torture and closure of Guantanamo Bay among steps including permitting US aid agencies to promote family planning after an eight-year hiatus.

The new president has also appointed envoys to the Middle East and Afghanistan-Pakistan.

In the midst of intense negotiations with Congress to push through an $825bn stimulus package, Mr Obama also on Monday offered a big boost to the environmental lobby by unblocking a Bush-era waiver that allows California and other states to impose higher carbon emission standards on industry.

The interview with Al Arabiya is likely to further antagonise conservative Republican critics of Mr Obama, who have already attacked his move to close Guantanamo within a year.