Tony Blair has insisted he can push through his reform programme despite suffering a surprise double defeat over new religious hate laws.
Mr Blair was absent for one of the crucial votes
MPs refused to overturn Lords changes which "watered down" the plans.
At prime minister's questions, Tory leader David Cameron said Mr Blair's reform plans could only go through if they were right and had Tory support.
Mr Blair joked about his latest defeat but said he could win Labour backing for school, welfare and police reforms.
Tuesday's vote was only the second time Mr Blair has suffered a Commons defeat as prime minister - the other loss came over the detention without trial of terror suspects.
He has more battles ahead over education reforms, identity cards and welfare reforms.
The embarrassment was made worse as Mr Blair missed one crucial vote on the hate laws after ministers misjudged the opposition.
On Wednesday, Mr Blair made light of his absence in one vote which the government lost by just one vote.
"I think for the education vote it is probably a good idea if I turn up," he told MPs.
He was urged by Mr Cameron to stop attacking freedom of speech, scrap his identity cards scheme and push ahead with plans to give schools more freedom.
Chief whip accused
Mr Blair said he would carry out his reforms because they were the "right agenda" for the country.
Chief whip Hilary Armstrong faces questions about what went wrong with the parliamentary arithmetic in Tuesday night's votes.
At least 15 Scottish MPs were allowed to be away from Westminster campaigning in the Dumferline and Fife West by-election. Another 26 MPs rebelled and others did not vote.
No 10 says Tony Blair has confidence in his chief whip
Mr Cameron ridiculed Ms Armstrong, saying: "She is probably the first chief whip in history to put the prime minister in the frame for losing a key vote, which is an interesting career move to say the least."
Earlier, the prime minister's spokesman said Ms Armstrong's job was not at risk, saying Mr Blair still had "enormous respect" for her.
The spokesman added: "Last night was just one of those things which went wrong."
An alliance of evangelical groups, atheists and comedians, including Blackadder star Rowan Atkinson, united against the Racial and Religious Hatred Bill.
They claimed it would curb free speech and even outlaw religious jokes.
Jews and Sikhs are already covered under race hate laws because the courts regard them as distinct races. The new offence would protect Muslims, Christians and other groups on the basis of their beliefs.
Ministers proposed a compromise which they said ensured people could debate, ridicule or insult religions as long as they did not intend to stir up hatred, or were "reckless" about stirring up hatred.
But MPs changed the wording of the government plans and backed peers by insisting the reckless behaviour should not be an offence.
Home Office Minister Paul Goggins accused opponents of playing politics, saying some of the architects of the Lords' changes backed the government's compromise plan.
"We have some choices to take in the weeks and months ahead about whether the political objective of the House of Commons is to defeat the government at every possible opportunity or whether it is to get the right policies," he said.
There were demonstrations outside Parliament against the plans
Mr Goggins said people should not lose sight of the fact that there was a new offence of incitement to religious hatred - albeit in a changed form.
Conservative shadow attorney general Dominic Grieve said the defeats were about good law, not political gain.
He branded the bill a "foolish manifesto commitment" introduced to "appease" some minority groups, and which had "threatened freedom of speech".
Liberal Democrat MP Evan Harris said: "The government just failed to understand that they can't take liberties with freedom of expression."
And Labour rebel Bob Marshall-Andrews said ministers had made an "awful misjudgement" in thinking they could get the plans through.
Mr Bean star Mr Atkinson said he could not be more pleased with the final version of the bill.
"With it, it seems to me, everybody wins," he said.