The Labour and Tory leaders have been holding talks with their backbenchers after their worst results for decades in the European elections.
Both were hit by a surge in support for Eurosceptic UK Independence Party.
UKIP more than doubled its 1999 vote to take 16% of the vote, in doing so pushing the Lib Dems into fourth place.
New UKIP MEP Robert Kilroy-Silk said he wanted to "wreck" the EU Parliament by exposing the waste, corruption and the way "it's eroding our independence".
Tony Blair told Labour MPs the party would have to focus on domestic issues like public services if it was going to win a third term.
According to a spokesman he said: "We have got to
have confidence in our arguments and hold our nerve and believe we will win."
The prime minister is said to have "robustly" rejected the suggestion of one MP that he should apologise for his decision to join the US-led invasion of Iraq.
Labour's vote fell 6% to 23%, their worst share of the vote since before World War I.
On course for Number 10?
The Tories got more votes - 27% - but that is still their lowest share of any nationwide election since 1832.
As Mr Blair met with the Parliamentary Labour Party, Michael Howard was addressing Tory MPs.
He told them the Euro elections were provided a platform for a Conservative general election victory.
Tory co-chairman Liam Fox said that if the European results were replicated at a national poll, Mr Howard would become premier.
The Liberal Democrats saw their vote rise 2% to 15% and stressed they were the only big party to increase their vote despite being pushed into fourth place by UKIP and winning 3% less of the poll than they did in the last general election.
In a good night for smaller parties, the Greens held their two Members of the European Parliament with 6% of the vote. The British National Party share of the vote is so far up from 1% in 1999 to 5%.
*Seat change is adjusted to allow a direct comparison with the results from the 1999 election
Elsewhere in Europe governing parties in Germany, France and Poland suffered big losses. As in the UK, Eurosceptic groups enjoyed their best result at the polls.
UKIP has quadrupled its number of MEPs from three to 12 with its best showing in the East Midlands, where it came within 0.3% of beating the Tories.
Ex-TV host Mr Kilroy-Silk pledged to get Britain back for the British people.
Asked what he would do when he sits in the European Parliament, Mr Kilroy-Silk said: "Wreck it - expose it for the waste, the corruption and the way it's eroding our independence and our sovereignty.
"Our job is to go there and to say 'look, this is what they do, this is how they waste your money, this how they spend it, this is how it gets corrupted, this is how they all go on this kind of gravy train and spend their time in the restaurants'."
All the results for England, Scotland and Wales have now been announced, with MEPs chosen by proportional representation in each region.
London: Labour and Tories drop a seat; UKIP gain an MEP; Greens hold their seat
North East: Lib Dems take a seat from Labour
Yorkshire and the Humber: Tories lose one seat to UKIP
Wales: No change in share of seats; Plaid Cymru vote dives by 12%
Scotland: Labour, Tories and SNP win two seats; Lib Dems, one
Northern Ireland:Ulster Unionists, Sinn Fein and the DUP each win a seat
South West: UKIP comes second with 23%, Labour end up in fourth place
South East: Labour and the Tories lose a seat each; UKIP gain an MEP; Greens retain their seat
Eastern region:Labour and Tories both lose a seat; UKIP gets two MEPs; Martin Bell's bid as an independent fails
West Midlands: Tories lose a seat to UKIP
East Midlands: Robert Kilroy-Silk becomes an MEP as the Tories narrowly beat UKIP into second place
North West: Labour and the Tories each drop a seat; Lib Dems and UKIP gain one each; BNP leader fails to get elected
In Scotland, Labour won two seats as did the Tories and the Scottish National Party while the Liberal Democrats won one.
In Northern Ireland, the Democratic Unionists, Sinn Fein and the Ulster Unionists claimed a seat each.
The results in Wales saw no change in the share of MEPs between the parties.
Labour is pleased with its Welsh showing, raising its vote by 1%. Plaid Cymru's vote dived by 12% and the Tories share dropped by 3%.
The overall EU turnout fell to an all-time low at 44.6%.
In the UK, 39% of voters went to the polls - topping the record of 37% for a European election set in 1989.
It is the first time the two largest parties have secured less than half of the vote between them.
Health Secretary John Reid told BBC Radio 4's Today programme the results were "disappointing" for Labour, but "disastrous" for the Tories.
Conservative shadow foreign secretary Michael Ancram said: "We are not as high as we would like but we are winning this election."
Voters were clearly telling Tony Blair they did not want him to sign the proposed European constitution, argued Mr Ancram.