The Chancellor and Clare Short, minister for international development, have requested the donation from an EU fund in order to rescue the "heavily indebted poor countries" (HIPC) debt plan announced with great fanfare by world leaders at their Cologne summit in June.
The financing of the programme to offer debt relief worth $100bn is still some $2bn short.
Ms Short said: "We have lost some of the momentum." It was essential to find the additional resources, she said.
Mr Brown will also call for private contributions from multi-national corporations, and could consider offering UK tax relief for such pledges. An announcement is due later this week.
The annual meeting of the International Monetary Fund, which starts in Washington at the weekend, will agree to use part of the Fund's gold reserves to generate around $2bn in funding for debt relief.
However, an earlier, controversial proposal to sell the gold on the open market has been shelved.
The two British ministers have written to Chris Patten and Poul Nielssen, the new EU commissioners for development and external relations respectively, asking for 1bn euros that have been accumulated without being spent in the European Development Fund.
The letter says: "This is a major opportunity for Europe to take a strong political lead on one of the great issues of our time."
The hope is that EU agreement can be secured ahead of the IMF meeting in order to trigger additional debt-relief contributions from other countries. The UK has already pledged $171m to the HIPC fund, and would add another $120m via the EU if the request is accepted.
The IMF and World Bank have agreed to ensure that debt relief is tied to specific policies to reduce poverty in the countries concerned. Aid organisations yesterday greeted this as an encouraging shift in the IMF's traditionally austere approach.
Mr Brown said it might only be a matter of weeks before some of the poor countries could start to feel the benefits of the new plan.
He said: "We want these to be seven days that have helped the world."