By Andrea Shalal, Rachel Savage and Jorgelina do Rosario

MARRAKECH, Morocco (Reuters) -The International Monetary Fund on Thursday hailed progress on a long-awaited memorandum on Zambia's debt restructuring, and said consensus was growing on thorny issues such as the comparability of treatment of private and public creditors.

IMF Managing Director Kristalina Georgieva told reporters the Group of 20 Common Framework for debt restructuring had been slow to deliver results, but welcomed the acceleration of timelines in recent individual country cases, including Zambia.

News about Zambia's imminent deal with its official creditors emerged during a panel on debt at the annual meetings of the IMF and World Bank.

Zambia Finance Minister Situmbeko Musokotwane, speaking on the same panel as Georgieva, said it has been "embarrassing to find ourselves in debt distress," which forced the country to cancel infrastructure projects it could no longer afford.

Georgieva also said she was more optimistic about the debt restructuring process now than before the creation of the Common Framework, but said more progress was needed.

"We should be concerned, but recognize that we are not at the footsteps of a debt crisis," she said.

Throwing out the Common Framework altogether would put the world in a "much less predictable environment," she told a news conference earlier in the day, adding that creative approaches were also needed, including moves to better align debt restructuring with the climate crisis.

A progress report on the debt restructuring discussions, published Thursday by the IMF, World Bank and India, the G20's current chair, found "significant progress" on actual debt restructuring cases, but said private and public creditors still had differences on the comparability of treatment issue.

"Assessing and enforcing comparability of treatment (CoT) between official bilateral and private creditors remains a divisive issue and no consensus could be reached among all stakeholders," the statement said.

The Global Sovereign Debt Roundtable met on Thursday, bringing together senior finance officials from the United States, China and other G20 countries, along with Zambia and other debtor nations, private sector creditors and the IMF and World Bank for closed-door talks on debt issues.

Zambia became the first African country to default in the COVID-19 pandemic era in 2020 but its restructuring under the G20's Common Framework process was plagued with delays.

It clinched an agreement in June to restructure $6.3 billion in debt owed to governments abroad including China and members of the Paris Club of creditor nations, but a formal memorandum of understanding (MoU) has taken months to complete.

Two sources familiar with the process said the negotiations took time but ultimately yielded a first: detailed language agreed by major creditor China with the Paris Club on how to enforce the comparability of treatment of private and public creditors.

"If indeed a better deal can be reached with the private creditors, then the deal with the official creditors is just off the table," one of the sources said. "That is the first time ever that China and the Paris Club have generated joint rules."

Progress in Zambia's case ould provide a model for subsequent debt restructuring agreements, the sources said.

China has said that its agreement with Zambia is not a blueprint, but the metrics to assess comparability and how to enforce it would create some precedent, the sources said.

(Reporting by Andrea Shalal, Rachel Savage and Jorgelina do Rosario; Editing by Sharon Singleton and Jonathan Oatis)