BRUSSELS — The International Monetary Fund said on Wednesday that it would contribute 1 billion euros, or about 10 percent, of a bailout package for Cyprus but stipulated that the country would need to take tough measures to overhaul its beleaguered economy.

The other 9 billion euros, or $11.6 billion, of the bailout is to come from the other 16 euro zone countries whose approval is still required.

“This is a challenging program that will require great efforts from the Cypriot population,” Christine Lagarde, the managing director of the I.M.F., said in a statement issued by the fund, which is based in Washington.

The commitment comes after the completion of a memorandum of understanding the fund has drafted with Cyprus and the other two international organizations involved in the bailout, the European Central Bank and the European Commission.