The prime minister has urged the Labour Party not to abandon New Labour's agenda, in what is expected to be his final new year message in office.
Mr Blair pledged to try to restart the Middle East peace process
Tony Blair did not refer to plans to step down, but said New Labour's "ambition and compassion" could bring it a fourth general election victory.
Despite facing its most difficult time in government, the party was dominating the battle of ideas, he said.
He also said Britain must "see through" the struggle in Iraq and Afghanistan.
Deputy Prime Minister John Prescott said Mr Blair's message showed that he wanted the "coalition between working and middle class voters" at the heart of New Labour to continue after he stands down.
Suggestions there was a disagreement between Mr Blair and his expected successor Gordon Brown about the future direction of the party were "a load of rubbish," he told BBC Radio 4's Today programme.
Mr Blair, who has said he will stand down by September this year, delivered his message while on a winter break in Miami with his family.
In the message, he spoke of a continuing threat from global terrorism which made it "so important that we see through the battles".
He also made a personal pledge to work towards restarting the peace process in the Middle East.
Mr Blair called on his party to be "restless, not complacent" in its search for ways to improve life in Britain.
"The Labour Party should take heart," he said. "It is dominating the battle of ideas.
"It will continue to do so provided it continues to be New Labour.
"Ambition and compassion: the combination of those instincts remain the basis of New Labour's three successive victories. They remain the basis of a fourth."
He listed plans that needed to be taken forward including reform in the NHS, in state education, of the pensions system and the energy supply network.
He said the economy needed to be even more dynamic in the face of the rising challenge from China and India.
Looking back at nearly 10 years as prime minister, Mr Blair said "real progress" had been made to address low investment and poor standards in public services, tackling crime, maintaining economic stability, reducing inequality and restoring national pride and confidence.
However, Conservative spokesman Chris Grayling said Britain was not getting the things that Tony Blair and Gordon Brown had promised.
"Mr Blair cannot be living on the same planet as the rest of us," he said.
"We are seeing hospital services cut around the country, rising violent crime, and the government is missing its own targets on education. Yet we are all paying vast amounts of extra money in tax."