UPDATE 2-Swedish PM could form new government after Centre Party drops rent reform demand

(Adds party comments, background)

By Anna Ringstrom and Simon Johnson

STOCKHOLM, June 23 (Reuters) - Swedish Prime Minister Stefan Lofven's hopes of surviving a political crisis looked brighter on Wednesday after his allies in the Centre Party said they would drop a contested proposal for rent reform.

Lofven has led a fragile centre-left minority government of Social Democrats and Greens, supported by former political rivals the Centre Party and the Liberals, since 2018.

The Centre and Liberals have pushed for rental reform, but the Left Party, whose support Lofven also needs, is against it and on Monday voted with the opposition to pass a no-confidence motion in the prime minister.

The vote meant Lofven had a week to resign or call a new election.

However, the Centre Party said on Wednesday that the plan for rental reform did not have majority backing and was therefore "not on the table anymore".

Party leader Annie Loof said she was open to renegotiating a formal policy deal with Lofven, dubbed the January Agreement, that has kept him in power until now.

"Now the Centre Party wants to see a new January Agreement which would cover the rest of the mandate period and give Sweden a government again," Loof said in a statement.

Dropping the proposal could bring the Left Party back on board.

'DIFFICULT' SITUATION

Left Party leader Nooshi Dadgostar said earlier this week that her party wanted Lofven back as prime minister, but without the plan to ease rent controls.

In a text to Reuters she said on Wednesday the political situation remained "difficult" but did not say whether her party now stood behind Lofven again.

Lofven welcomed the Centre Party's decision to abandon rent reform.

"It is important that more parties now do what is best for the country," he said in a text to Reuters.

Even if the Left Party drops its opposition to the government, Lofven still needs support from the Liberal Party, which abstained in the vote of no-confidence, to form a viable government.

In an emailed statement, Liberal Party spokesman Mats Persson said the party sought a liberal, right-of-centre government, adding: "That is the best for Sweden."

A spokesperson for Lofven said that his Social Democrat party was holding discussions "on a broad front", but gave no further details.

Sweden is due to hold a regular election in September 2022. (Reporting by Anna Ringstrom, Simon Johnson and Johan Ahlander; Editing by Alexander Smith and Gareth Jones)