The threat posed by terrorism is a "struggle for the soul of the 21st Century", Gordon Brown has said.
Mr Brown and Mr Bush vowed cooperation in counter-terrorism
"It is a war. We have had to fight a very big campaign," he said in an interview with NBC Nightly News.
Mr Brown, who was on his first official visit to the US since becoming UK prime minister in June, had been asked why he did not use the phrase "war on terror".
He has denied that his view of terrorism differs greatly from that of US President George W Bush.
The phrase "war on terror" is now rarely used by the British government - but in an interview with the US TV network NBC, Mr Brown said of the fight against terrorism: "This is a battle, this is a struggle.
"It's a struggle for the soul of the 21st Century."
His trip has included talks at Camp David with President Bush in which they renewed pledges to fight terrorism and to seek progress in Iraq.
He has also praised the US, saying the world owed it a debt for "its leadership in this fight against international terrorism".
While their language at Camp David, differed both agreed the counter-terrorism fight was "akin to the Cold War".
Mr Brown told NBC: "I have got no doubt we are facing major campaigns by al-Qaeda inspired terrorists.
"We know a large number of people would, if they could, destroy life and put at risk our infrastructure and we have got to be vigilant."
He also said there would be no change of policy on Iraq and said an "artificial timetable" for the withdrawal of British troops would be "a mistake".
"We continue to do what we have been doing over these last few months and in these last few years," he said.
He has said any pullback of troops to an "overwatch" role would be made "on the military advice of our commanders on the ground".