ATHENS, Greece — Greece’s government has made new concessions in talks with its creditors, though some European officials said they were still not good enough and that a deal was nevertheless impossible before a Greek referendum on Sunday.

Prime Minister Alexis Tsipras sent a letter Tuesday night, just hours before the country’s bailout program was due to expire, saying his government was prepared to accept creditors’ proposals made last weekend, subject to certain amendments.

The creditors did not accept Greece’s new overture, leaving the country’s bailout program to expire. But eurozone finance ministers will meet today to discuss the terms again. Hopes that Tsipras was softening his position — after refusing for five months the spending cuts that creditors had demanded in exchange for loans — boosted markets today.

But German Finance Minister Wolfgang Schaeuble was clear that no deal was imminent, at least not before Greece holds a popular vote on the creditors’ proposals on Sunday.