MOSCOW, Oct 29 (Reuters) - Two Roman Catholic priests, one Russian and one from Ecuador, have been found dead in a Moscow apartment amid signs of an attack, investigators said on Wednesday.

The bodies of the two Jesuits were found by police late on Tuesday in the apartment owned by their order in the upmarket Petrovka Street, the Investigative Committee of the Prosecutor-General's office said in a statement.

The Russian priest led the country's Jesuit order, registered there as the Russian Independent Region of the Society of Jesus.

"Investigators have launched a probe into the murder," the statement said. "(The priests) had skull and brain injuries. Forensic experts have established that they died more than a day before."

Father Igor Kovalevsky, Secretary General of the Catholic Bishops' Conference in Russia, named the two as Otto Messmer, a Russian national, and Ecuadorean priest Victor Betancourt.

"The murder of two priests at once is something exceptional," Kovalevsky said. "But killings of priests, including Catholic ones, have happened in Russia before."

Kovalevsky said several years ago a Catholic priest of Slovakian origin was murdered in the town of Bryansk in western Russia. "As for the motives, in previous cases it was purely crime, like robbery," he said.

The apartment where the Catholic priests' bodies were found is in one of Moscow's most exclusive districts, a short walk from the Kremlin and the Bolshoi Theatre.

The Investigative Committee said the door to the apartment was found open but there were no signs that property had been stolen.

"The investigation is considering all possible versions of what could have happened, including a domestic crime, because the room bore signs of a party," it said.

Several Russian Orthodox priests have been killed across Russia in the past few years. Prosecutors blamed those attacks on criminals seeking to steal icons and other church property. (Reporting by Alexander Gelogayev and Dmitry Solovyov; Writing by Dmitry Solovyov; Editing by Louise Ireland)

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