"We have made clear that governments that sponsor terror are as guilty as the terrorists and will be held to account," Bush said without naming any country.
The US president also voiced his anguish over terrorists continuing to pose "serious challenges as the world saw in the terrible attack in Mumbai last month".
"We must stand by the friends and allies who are making tough decisions and taking risks to defeat the terrorists. We must keep up the pressure on regimes that sponsor terror and pursue weapons of mass destruction," Bush said in a speech at the United States military academy West Point in New York on Tuesday.
"For many years, America treated terrorist attacks as isolated incidents and responded with limited measures," Bush said. But the US changed its strategy after the September 11, 2001, terror attacks and within weeks its armed forces began taking the fight to the terrorists around the world and "we have not stopped".
Though the global war on terror launched after the 9/11 attacks weakened, "the terrorists continue to pose serious challenges, as the world saw in the terrible attack in Mumbai last month", he said.
"Al Qaida's top two leaders remain at large, yet they are facing pressure so intense that the only way they can stay alive is to stay underground. The day will come when they receive the justice they deserve," Bush said while on a visit to the West Point Military Academy in New York.
"... After 9/11, we applied the doctrine to Afghanistan. We removed the Taliban from power. We shut down training camps where Al Qaida planned attacks on our country. We liberated more than 25 million Afghans. Now, America and her 25 NATO allies and 17 partner nations are standing with the Afghan people as they defend their free society," Bush said.
"The enemy's determined; the terrain is harsh; But our coalition will stay in this fight. We will not let the Taliban or Al Qaida return to power. And Afghanistan will never again be a safe haven for terrorists," he added.
The US president said even from an ideological point of view the rejection of violent extremism has started gathering traction.
"Muslims from Jordan and Turkey, to India and Indonesia have seen their brothers and sisters massacred and recoil from the terrorists. And even within the jihadist ranks, religious scholars have begun to criticise Al Qaida and its brutal tactics. In these ideological rejections we see the beginning of Al Qaida's ultimate demise," Bush said.