"A more representative, responsive and accountable governance structure is essential to strengthening the IMF's legitimacy," Geithner said in a statement.
He noted that G-20 countries had committed to shift some control in the International Monetary Fund from countries with strong representation to those with little input. The Group of 20 includes developing economic powerhouses such as China, India and Brazil.
Geithner said the IMF should outline how the proposed transfer of at least 5 percent of voting power within the institution can occur.
"We call on the IMF to facilitate this process by providing scenarios of how the quota shift could be implemented in the very near-term," he said.
The remarks came at the IMF's annual meeting, held this year in Istanbul. They followed a decision at a Pittsburgh forum that the Group of 20 nations would become the world's main economic decision-making forum, effectively taking over the role of the G-7 group of rich countries.
Geithner said reform of the IMF's executive board was vital to modernizing the Washington-based institution, which represents 186 countries. The U.S. recommends reducing the board size while preserving the current number of emerging market and developing country chairs.
The IMF is usually headed by a European and the World Bank by an American. It has received pledges of more money to help poor countries struggling to emerge from the global economic crisis, and a broader range of nations wants to have more say in how the funds are handled.
Aid agency OXFAM says current voting formulas at the IMF give Luxembourg more weight than the Philippines, which has almost 200 times the population. It said the 5 percent shift in voting power was insufficient.
"They need to give more voice to the poorest countries, have fewer European seats on the Board, and get rid of the U.S. veto," said Caroline Pearce, OXFAM policy adviser. She said the IMF can only be relevant if it gives "countries hardest hit by the financial crisis a say in their own destiny."
The U.S. has a 17 percent voting stake in the IMF, effectively giving it veto power because major decisions require an 85-percent majority to pass.
In the past, the IMF has been criticized for allegedly imposing austerity measures on countries in exchange for loans and without sufficient regard for the impact on the poor.
IMF officials say they have shown more flexibility in recent years. John Lipsky, the IMF's No 2. official, has said the IMF is undertaking "substantial efforts" toward internal reform that will provide "a fair shake for all our members."
At the Istanbul conference, a group of 35 heavily indebted countries welcomed the G-20's new role as a leader in global economic decisions, but said poor nations also needed representation to express their financing needs.
"We need at least one seat so that almost 1 billion Africans can express their views," said Lazare Essimi Menye, Cameroon's finance minister.
Associated Press Writer Suzan Fraser contributed to this report.