By Michele Kambas

ATHENS (Reuters) - Greece on Monday unveiled plans to revise its constitution, formally proposing a clearer distinction between the state and the powerful Orthodox Church, changes in how the president is elected and limiting terms of lawmakers in parliament.

Left-wing Prime Minister Alexis Tsipras said the proposals were aimed at transforming a system full of "pathogens", and public feedback would be sought from September before the plans are put to parliament for further consultation.

"We aspire to see a process of active participation of citizens, and not something which is restricted within four walls of parliament," Tsipras told state officials during a presentation.

Under the proposals, the president - now a ceremonial role - would be elected in a national vote if there were a lack of consensus among members of parliament, who currently pick the head of state.

There could also be a "moderate" increase in the powers of the country's president on issues such as having the right to refer legislation to experts for legal ruling, Tsipras said.

Lawmakers would be restricted to two consecutive terms or eight years in office, a new court would be formed to rule on the legality of legislation, and there would be the conditional abolition of parliamentary immunity.

Tsipras, who, along with many in his cabinet, eschewed the tradition of taking a religious oath when he was sworn in, said the role of the Church in Greece was an "exceptionally sensitive issue".

Greek Orthodoxy is considered the country's official religion.

"I think establishing religious neutrality of the state is a mature demand, maintaining for historical and practical reasons the role of Orthodoxy as the prevailing religion, Tsipras said.

Constitutional reforms have been a rallying cry of Tsipras's government since his left-wing Syriza party swept to power in early 2015 on a tide of anti-austerity sentiment by a public clobbered by years of economic reforms and financial bailouts.

But Tsipras was forced to cave in and accept a third international bailout within months last year as the country teetered on the brink of a fiscal cliff and threat of getting thrown out of the euro zone.

Other initiatives would be to allow referendums related to "national issues" or in pursuing items of legislation.

It could not apply to fiscal matters, Tsipras said.

(Reporting by Michele Kambas; Editing by Alison Williams)