'Ambition and commitment'
Barroso said he would only take up another term if EU leaders accept a stronger role for his executive and the EU.
He said: "We are not living in business-as-usual times. We need ambition and European commitment."
Many leaders had already endorsed Barroso, but he had waited for the results of the election, which ran from June 4-7, before announcing a decision.
Anglea Merkel, the German chancellor, said: "We already said that Mr Barroso has our support, at least from my side."
All 27 EU leaders must agree on the choice of president and Barroso has been lobbying Merkel, Nicolas Sarkozy, the French president, and other leaders in recent months, to secure a second term.
Fischer said he would go to member nations to build consensus on Barroso's bid before an EU summit next week in Brussels.
Along with unanimous backing from EU leaders, Barroso will need the endorsement of a majority of European Parliament politicians.
The president of the European Commission presides over an executive team of 26 commissioners drawn from each of the bloc's member states.
The commission is responsible for drafting new laws and ensuring member states abide by existing ones.