President Barack Obama emerged from Hawaiian seclusion on Monday to reassure the American public and quell gathering criticism as a branch of al-Qaeda claimed responsibility for the thwarted attack on an American passenger jet on Christmas Day. Obama vowed to track down all who were involved in helping a Nigerian man who tried to set off explosives aboard a Northwest Airlines flight as the plane approached Detroit,acknowledging the growing conclusion that the act was not that of a lone wolf but of a trained Qaeda operative. With more signs pointing to Yemen as the origin of the attack,the White House was weighing how to respond. The President broke his silence as debate about the episode turned increasingly political. An assertion over the weekend by Janet Napolitano,Homeland Security Secretary,that the system worked drew strong criticism and forced her to recalibrate it. On the international front,a group called al-Qaeda in the Arabian Peninsula,which operates in Yemen and was the target of a recent airstrike facilitated by the US,asserted that it had sponsored the attempted attack in retaliation. US officials said they considered the statement,which was posted on jihadist websites,credible. The Yemeni government said Monday that the suspect in the failed bombing had spent four months in the country before leaving in December. Obama,making his first public comments since the episode,said he had ordered his national security team to keep up the pressure on terrorists. He vowed to use every element of our national power to disrupt,dismantle and defeat the violent extremists who threaten us,whether they are from Afghanistan or Pakistan,Yemen or Somalia,or anywhere where they are plotting attacks on the US homeland. He assured Americans he was on top of the situation. We will not rest until we find all who were involved and hold them accountable, Obama said. The visual contrast of a President on vacation while there was anxiety about air travel also drew fire. Although aides issued statements describing conference calls with counterterrorism advisers,pictures of passengers enduring tougher airport screening were juxtaposed with reports of the President picnicking at the beach and playing sports. Obamas appearance coincided with new evidence linking Nigerian suspect Umar Farouk Abdulmutallab,23,to al-Qaeda. The statement by al-Qaeda in the Arabian Peninsula,accompanied called him a hero who had penetrated all modern and sophisticated technology and devices and security barriers in airports of the world and reached his target.