Christine Lagarde has refused to say whether she will seek a second term as head of the International Monetary Fund after both Britain and Germany gave her their backing.
Chancellor George Osborne issued a statement saying the Government had nominated her to stay in the post.
The German government quickly followed, with a finance ministry statement saying Ms Lagarde "was a circumspect and successful crisis manager during the difficult period after the financial crisis".
Countries normally nominate their preferred candidate before the individual declares their intention to run.
At a panel in Davos, Switzerland, where the World Economic Forum is being held, Ms Lagarde said she was honoured but did not want to confirm whether she would agree to stand again.
The IMF has typically been run by a European official, while its sister organisation, the World Bank, by an American. Developing countries have increasingly opposed this informal arrangement.
The IMF's recent downgrade of growth forecasts and Ms Lagarde's future are on many minds at this week's World Economic Forum gathering, where she is a prominent presence.
Mr Osborne said: "At a time when the world faces what I've called a dangerous cocktail of risks, I believe Christine has the vision, energy and acumen to help steer the global economy through the years ahead."
The World Economic Forum meeting of business leaders and public figures has been overshadowed by turmoil in global markets and geopolitical security issues.
Speaking about China's economic slowdown, Ms Lagarde said the country needed to refine its communication on reforms it was taking and its market policies.
A Chinese market regulator said the concerns over growth were overstated. He said China has no option but to support growth this year, using its large financial reserves if needed.
"We cannot afford to let the growth rate fall too sharply, because that would ignite a lot of financial problems inside China. So we will have appropriately expansionary fiscal and financial policy this year," said Fang Xinghai, from China's Central Leading Group for Financial and Economic Affairs.