CAIRO, July 3 (Reuters) - Egyptian President Mohamed Mursi's hardline Islamist allies in al-Gamaa al-Islamiya want him to call early presidential elections to avoid bloodshed and a military coup, Tarek al-Zumar, a senior member of the group told Reuters.

The Gamaa Islamiya, once an armed group that is one of Mursi's few remaining allies, had been advising the head of state to call early presidential elections in the two days since the army issued a deadline for politicians to resolve the political conflict by Wednesday.

"This peaceful, constitutional transfer (of power) will spare blood," Zumar told Reuters by telephone, adding that it would also protect the constitution that was passed into law in December.

He said the army's statement appeared to presage a coup, but this "can be avoided if the president decides to hold a referendum on early presidential elections". (Reporting by Tom Perry; Editing by Paul Taylor)