QUITO, May 21 (Reuters) - Ecuador's assembly extended its deadline to rewrite the country's constitution by two months late on Tuesday, a move that could further hurt the powerful body's popularity.

The government-controlled assembly was due to finish work on the new charter next week but it still has hundreds of articles to draft.

The constitution must be ratified by Ecuadoreans later this year. It will be a key vote for President Rafael Correa, with the assembly expected to call an early general election.

The assembly's popularity has dropped as many people see it bogged down in debate and not solving everyday problems like unemployment and inflation, analysts say.

The body's approval rating was 37 percent in April, a drop of 25 points since it started work in November, pollster Cedato-Gallup showed in a recent survey.

"However, the president remains immune to the political fallout of the assembly," said Franklin Ramirez, a professor with Ecuador's branch of the Latin American Faculty of Social Sciences. "He still does not face a serious challenge from the opposition."

The assembly is acting as the legislature and has approved a wide range of constitutional changes, laws and decrees that would help Correa consolidate his leftist government.

A weakened opposition says Correa is using the assembly to amass dictatorial powers.

Correa says a new constitution is needed to rein in elites benefiting from current laws and to bring stability to the Andean country that has seen three presidents toppled in just over a decade.

There have been no opinion polls yet showing whether Ecuadoreans favor the changes. (Editing by John O'Callaghan)