The UK is proposing to cut the EU's spending on aid to poorer countries in an attempt to get a deal on the bloc's future budget by the end of December.
Mr Blair expects support from other net contributors to the EU budget
The move would hit hardest the Eastern European states which joined the EU last year, but Italy has also objected.
The last talks on the budget ended in crisis in June, when the UK refused to give up its £4bn (6bn euro) rebate.
Under the new deal, the UK would give up part of its rebate in return for a lower overall level of spending.
European diplomats are quoted as saying that the UK is proposing a budget for 2007-13 capped at 1.03% of EU gross national income.
This compares with a proposal of 1.06% put forward by the last holders of the EU's presidency, Luxembourg, last June.
BBC Europe Editor Mark Mardell says the new British proposal would mean a 10% cut in the money that is spent on projects like roads, rail and water treatment in the 10 countries which joined the European Union last year.
A Commission spokesman told the Reuters news agency that rural development funds for some older member states would also be cut.
Polish Regional Development Minister Grazyna Gesicka said she was "disappointed" by the British proposal.
European Commission spokesman Johannes Laitenberger said: "It is clear that it is not those most in need which have to bring forward the biggest sacrifices."
And Italian Foreign Minister Gianfranco Fini, who holds talks with his UK counterpart Jack Straw in London on Wednesday, said his country would not accept any reduction in regional aid for southern parts of the country.
However, a European diplomat said the British proposal was balanced by measures to ensure that new members were able to absorb the money they were allocated.
"If we get a deal, then the people who benefit most from that deal are the accession countries, both in terms of the certainty and the ability to get their money," said Mr Blair's official spokesman.
UK Prime Minister Tony Blair travels to Estonia and Hungary on Thursday and Friday to sell the idea to seven of the 10 states.
Our Europe Editor says the British are calculating that the new member states would prefer to have some money to spend soon, rather than delay EU-funded projects because there is no budget deal.
It is expected the big payers into the EU, such as Germany, the Netherlands and Sweden, will back the plan and that France and Spain will object, he adds.
Retreat on CAP
In June, the UK said it would only agree to Luxembourg's proposal to freeze the UK rebate if it won guarantees of major cuts in farm spending.
However, reports suggest it has failed to win support for further changes to the Common Agricultural Policy during the 2007-13 budget period, and is now changing tack.
"Sources close to Mr Blair believe that losing some of the rebate won by Mrs Thatcher will be acceptable to the public if there is overall reform of the European Union's budget," our Europe Editor reports.
The UK will formally unveil its proposal next week, and hope to win the support of the 24 other member states at a summit on 15 and 16 December, two weeks before the end of its EU presidency.
The new member states have consistently urged the older states to reach agreement on the budget quickly, because delays will hinder their attempts to plan how to spend the money.
This, in turn, will affect how much of the money available to them they are actually able to make use of.