Mr Blair said he plans to press ahead with his planned reforms
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The prime minister has admitted he faces a "rough ride" in trying to get his plans to reform schools and hospitals through Parliament.
But Tony Blair says he and his senior ministers are determined to press ahead with the proposals.
He told the News of the World that he and the Cabinet had agreed to "continue doing what is right, not what is easy".
Chancellor Gordon Brown has said the Labour party has to "listen and learn" and try to connect with the public.
He told the Independent on Sunday the government had to "work at it" to get its programme of reforms through Parliament.
Bill defeated
Mr Blair's comments follow the rejection of plans to allow terror suspects to be held for up to 90 days without charge.
The plans were defeated by 31 votes, with 49 Labour MPs rebelling against the government, on Wednesday.
It marked Mr Blair's first House of Commons defeat as prime minister.
The Commons instead backed a compromise proposal to extend the detention time limit from the current 14 days to 28 days.
Despite this setback, Mr Blair says is not prepared to back down over planned public service reforms - despite opposition from some Labour MPs.
Brown said the government and Labour MPs had to unite
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Writing in the News of the World, he describes how he has taken "tough decisions" during the government's time in power.
He adds that "more needs to be done if we are to meet our ambitions for this country and its people".
In the article, the prime minister suggests the government's programme of reforms will target education, hospital waiting times, pensions and welfare benefits.
"All of this will require more difficult decisions and strong leadership....but there is no doubt it will be worth it if, as a result, Britain is better, fairer, and stronger," he says.
Trust schools
This week Mr Blair will launch a campaign to gather support for the government's schools white paper.
On Friday he will campaign on the education plans in the north of England with David Miliband, Alan Milburn and education minister Lord Adonis.
He is also expected to hold a series of meetings with small groups of Labour backbenchers to discuss his plans regarding schools.
Many Labour backbenchers are thought to be unhappy with plans for trust schools, which would be self governing and independent of local education authorities.
Mr Brown said Labour MPs and the government had a "duty" to work together to avoid future defeats, saying they could not afford to rely on Tory support to push through bills.
"We need to listen to people. We have to listen and learn and talk to people round the country and that is why I am going round the country to listen and visit the regions and listen to what people say," Mr Brown said.
He said it was not the time to discuss "personalities or individuals", which is thought to be a reference to Mr Brown's expected takeover as prime minister.