Christine Lagarde is involved in a struggle to raise funds for the International Monetary Fund amid fears that a fresh eruption of the global financial crisis will leave the organisation short of emergency cash.

The fund's managing director was lobbying hard for Britain and other developed nations that have yet to pledge money to build a bigger firewall to provide more than $400bn (£250bn) in fresh resources.

George Osborne, who arrived in Washington on Thursday night for the spring meetings of the IMF and the World Bank, has yet to say whether the UK will participate in the fundraising exercise, insisting that the eurozone must show a willingness to sort out its own problems first.

With the US refusing to participate in the fundraising exercise, the IMF has already scaled down its target from the $600bn it was looking for when the eurozone crisis was at its height in late 2011.

But the upward pressure on Italian and Spanish borrowing costs has raised the prospect that the eurozone's third and fourth-biggest economies might need financial support, providing extra ammunition for Lagarde as she asks for loans both from developed nations and the leading emerging economies.

IMF sources said that they did not expect the US to respond to the call in an election year, since any loan made would have to be passed by both houses of Congress. Lagarde said she wanted the US to play its part in the international effort to combat future crises. "The leading economic power in the world clearly has to have a leadership role," she said.

Lagarde added that Europe needed to keep up the pace of reform and should aim for a "deepening integration of the eurozone".

She expressed concern about five "dark clouds" – high unemployment, slow growth, over-rapid deleveraging by banks, strains in the eurozone and higher oil prices – gathering over the global economy. She said she was looking for further support from "our broader membership" to ensure that it could tackle crises and ensure global financial stability.

"The fund needs to participate in building additional firepower to the global firewall we have been advocating. I expect our own firepower to be significantly increased."

So far, the eurozone has pledged $200bn to the IMF, Japan $60bn and Switzerland $26bn. Four other European countries – Norway, Sweden, Denmark and Poland – have between them agreed to contribute $35bn.

With concern growing about the health of Spain's banks, Lagarde said she wanted the European authorities to be able to invest directly in financial institutions rather than through governments.

Robert Zoellick, the president of the World Bank, said the impact of the European debt crisis was rippling out to poorer countries in the Balkans, south-east Europe and north Africa. "The eurozone is going to be walking a very fine line," he said, adding that the European Central Bank (ECB) had only bought time by providing cheap three-year money to eurozone banks. "That time has to be used. There needs to be a focus, not just on austerity and macro-economic stability, but on growth."

Zoellick said the phase in which banks were able to use the low-cost funds from the ECB to purchase government bonds was coming to an end. "Italy and Spain are vital," he added. "We are not out of this mess yet. It is still a fragile economy."

The World Bank president said that the outcome for the eurozone would depend on actions taken in individual countries and the structural reforms they implemented. "It is very difficult to take these steps in a no-growth environment."

Zoellick, who will be leaving the World Bank in the summer at the end of his five-year term, expressed concern that the new rules for banking regulation drawn up under the Basel III agreement were too tough and would choke off lending. "Basel III is too strict in my view," he said.