COLOMBO, June 27 (Reuters) - The International Monetary Fund (IMF) said on Thursday that Sri Lanka's agreements with China and other creditor nations to restructure about $10 billion in bilateral debt took the island nation a step closer towards restoring debt sustainability.

"We hope that there will be swift progress on reaching agreements with external private creditors in the near future," Peter Breuer, IMF's senior mission chief for Sri Lanka, said in a statement.

Sri Lanka still needs to convince bondholders to restructure about $12.5 billion in international bonds. (Reporting by Uditha Jayasinghe, Writing by Sudipto Ganguly; editing by Kim Coghill)