In what the London-based paper describes as an interview, Omar vowed the wrath generated by the U.S.-led war in Afghanistan would reach the White House.
Al-Sharq al-Awsat said Badi Qarhani recently interviewed Omar in the mountains of Afghanistan, with Omar's press adviser giving written replies to Qarhani's questions.
Omar and bin Laden have so far frustrated United States and coalition efforts to find and seize them, and Washington admits it does not know their whereabouts.
Omar described the Sept. 11 terrorist attacks that leveled New York's World Trade Center and damaged the Pentagon near Washington as "undoubtedly one of the most important events in history."
"These attacks had a major role in reshuffling the cards of international politics, " Omar said.
American authorities regard bin Laden as responsible for those attacks and has responded by leading a coalition against the extremist Islamic Taliban regime that ruled Afghanistan from 1996 until being driven from power last year.
"We do not consider that the wars in Afghanistan and Palestine and other Islamic countries are over," Omar said. "As for Afghanistan, I say that the battle has just started, and its fire and wrath will reach the White House because that is the center of injustice and oppression from where the war against Islam and Muslims was launched without any legitimate international justification."
Omar vowed the U.S. presence in Afghanistan "will be hell because Osama bin Laden was still alive and that is a sore in the heart of (President) Bush who had promised his people he would kill the al Qaida leader."