BRUSSELS (Reuters) - Eurogroup chairman Jeroen Dijsselbloem said Friday's bailout deal would put Greece's debt on a sustainable path and followed very constructive cooperation with the Greek government.

In a briefing following around six hours of talks in Brussels, Dijsselbloem also said he was optimistic the International Monetary Fund would be willing to take part.

"I think there is reason for optimism," he said.

Greek Prime Minister Alexis Tsipras faces a rebellion from his leftist lawmakers following the Greek parliament's approval of a new bailout program, forcing him to consider a confidence vote that could pave the way for early elections.

Among the sharpest critics of the new bailout deal has been former Greek Finance Minister Yanis Varoufakis, who was removed from the talks early last month.

"After the changes in the government and the crises that we had, the cooperation with, let's say, the changed Greek government is very constructive, very well organized," Dijsselbloem said.

Among the amendments to an outline deal that helped to clinch Friday's agreement was wording to make crystal clear that depositors would be protected.

Greek leaders have repeatedly dismissed the possibility they will have to bail in depositors to prevent the collapse of the banking system.

"In the memorandum of understanding, there is nothing on bail-in. Bail-in has to be clear to everyone. It has to be clear, this is how it's going to work. Depositors will be exempted."

(Reporting by Alastair Macdonald and Barbara Lewis; Editing by Kevin Liffey and James Dalgleish)