The Conservatives have made a significant step towards recovery, party leader Michael Howard said as he conceded Labour had won.
Michael Howard says his campaign has sent Labour a message
Mr Howard was speaking after the Tories won seats from Labour and the Lib Dems, including Enfield Southgate from Schools Minister Stephen Twigg.
With few declarations to come, they have 196 seats - up from 166 in 2001.
However, Labour adviser Alastair Campbell said the Tories remained "flat on their backs".
At the count for his Folkestone and Hythe seat in Kent at about 0420 BST, Mr Howard conceded Labour had won the election and congratulated his opposite number.
He said he would give the prime minister his "full support" if he delivered on the people's priorities of cleaner hospitals, school discipline, controlled immigration, value for money and more police.
"The time has now come for action not talk from him," he said.
Mr Howard said the Tory campaign had "sent a message" to Mr Blair.
"For the Conservative Party it marks a real advance towards our recovery," he said.
"The task which faces us in the next Parliament is to complete that recovery and it is a task I am sure everyone in the Conservative Party will address with real relish."
Former Tory education spokesman Tim Collins, narrowly beaten in Westmorland and Lonsdale by the Lib Dems, said his party could have won more seats with a more positive campaign.
"You have to engage with the other side on the most important issue - which is the economy."
But former Tory Foreign Secretary Malcolm Rifkind said Mr Howard had "earned his right" to lead the party into the next election.
He said Mr Howard should be judged on his energy and his leadership, rather than his age.
And he said it was right to make immigration an issue as neglecting it would create a vacuum that would be "filled by the wild men of the BNP".
Labour is predicted to win a majority of 66, down from 167 in 1997.
The Tories enjoyed major successes in London, including notable wins in Putney, Enfield Southgate - famously lost by Michael Portillo in 1997 - and Croydon Central.
Putney provided the first Conservative win of the night, with finance manager Justine Greening overturning Tony Colman's 2,771 majority to win the seat by 1,766 votes.
The Tories unseated Constitutional Affairs Minister Chris Leslie in Shipley and Health Minister Melanie Johnson in Welwyn Hatfield.
Tory frontbenchers Theresa May, Oliver Letwin and David Davis all thwarted the Lib Dem "decapitation strategy" aimed at toppling them.
The Lib Dems also inflicted Conservative losses in Taunton and Solihull.
The Conservatives and Mr Howard lauded the election of their first black MP, Adam Afriyie in Windsor.
The leader was also pleased to see an Asian Tory MP, as well as more Conservative women, elected.
The Conservatives have gained two toeholds in Wales by winning Monmouth and Preseli Pembrokeshire from Labour.
A surprise victory in Dumfriesshire saved the party from a complete wipe-out in Scotland.
Peter Duncan, the only Tory MP in Scotland in the last Parliament, failed to win in Dumfries and Galloway.
In Croydon Central, the Tories made a gain from Labour by just 75 votes after three recounts.
In 2001, the Conservatives won 166 seats, just one more than their showing four years earlier.
Labour Cabinet minister Margaret Beckett said she had a "horrid feeling" immigration had helped the Conservative effort in this election.
Ex-Tory Cabinet minister Ken Clarke denied immigration had featured highly in the campaign, but said he would have liked more debate from all parties on the economy, healthcare and education.