The U.S. holds close to 17 percent of the vote. As a group European countries, including Nordic countries, hold somewhere between 40 to 47 percent of the voting sway on the board.
Countries such as Egypt, Indonesia, South Korea, Russia and French-speaking African nations early on declared their support for Lagarde, but represent marginal voting power.
The IMF job fell vacant after the sudden resignation of Dominique Strauss-Kahn, who has been charged with sexually assaulting a hotel maid in New York. He denies the charges.
Although a self-proclaimed long-shot candidate, Carstens has vigorously campaigned on his experience as a former IMF official, as well as dealing with developing world economic crises.
He has the backing of all of Latin America, with Peru and Chile endorsing him on Friday. While Brazil has been silent on whether it supports him or not, IMF board officials expect it to join the rest of the region.
Supporters of Lagarde cite her political and economic credentials throughout Europe, which is the focal point of IMF efforts to head off another global economic downturn.
Both candidates have committed to more voting power for emerging economies and even-handed advice to both advanced and developing countries.
Developing nations want their growing clout in the global economy reflected at the IMF, but have won only modest increases in voting power so far.
The continuing inability to mount a serious challenge to Europe's dominance in the IMF caused two potential contenders -- former Turkish Economy Minister Kemal Dervis and ex-South African Finance Minister Trevor Manuel -- to decide against running.
Before his downfall in May, Strauss-Kahn oversaw a shift in voting power that gave emerging markets greater say but not as much as they wanted. He named a Chinese special advisor, a step short of giving Beijing a coveted deputy managing director post.