Mr Blair used a speech to the Trades Union Congress annual dinner to affirm that the Government would not bow to demands to legalise secondary industrial action and insist that unions must modernise to meet the challenge of competition from the Far East.
He spoke just hours after Mr Brown delivered a trenchant message on the TUC conference platform, clearly indicating that unions could not expect a radical change in position if the Chancellor is confirmed as Mr Blair's successor.
The Prime Minister said: "I understand the strong feelings caused by the Gate Gourmet dispute. But it would be dishonest to tell you that any Labour government is going to legislate a return to secondary action. It won't happen."
However, he made an offer to work with unions. He told the gathering of senior union leaders: "What you don't need is another round of publicity about the usual demands on the Labour government met with the usual refusals. What you and we both need is an agenda of practical engagements with people at work, helping them manage the forces of change."
Mr Blair echoed Mr Brown, pointing to the "urgent" challenge from fast-growing Asian economies such as China and India.
He said: "They will impose a competitive pressure on us that it is pointless to question. It is reality. So let us face it and work together in partnership.
"The alternative is no alternative at all. It is a decision to decline."
Earlier Mr Brown told TUC delegates that there must be no return to the industrial "conflicts and disorder" of the past. The Chancellor rebuffed union demands for a relaxation of laws banning secondary industrial action.
The Chancellor's speech won only lukewarm applause from delegates, while union leaders warned that he would have to offer more to secure their backing.
Mr Brown said: "If we are to succeed there must be no return to the fiscal irresponsibility, the economic short-termism, the inflationary pay deals and the old conflicts and disorder of the past.
"There can be no retreat from demanding efficiency and value for money as well as equity as we renew and reform public services."
Mr Brown laid out a package of full employment, economic stability, but uncomfortable reform to the union leaders, who have demanded a sharp change in Labour's direction when Mr Blair stands down.
However, he offered the leaders reassurance when he pledged that the Government would introduce legislation to honour the Warwick agreement in full.
But Derek Simpson, the general secretary of Amicus, said: "He'll have to go a lot further to secure the unequivocal backing if the trade union movement. He said nothing to indicate that he is serious about winning over working people and their representatives in a forthcoming election for the Labour leadership."
Tony Woodley, the leader of the Transport and General Workers' Union, said: "He didn't really tackle the big issues which are critical to the union movement. It was the usual Brown speech, that's why he got a flat reception."
However, Dave Prentis, the general secretary of Unison, said: "The Chancellor said many of the things we want to hear, particularly his emphasis on honouring the Warwick agreement."Reuse content