By Maria Carolina Marcello and Anthony Boadle

BRASILIA (Reuters) - A constitutional amendment proposed by interim President Michel Temer to put a ceiling on Brazil's public spending will pass the lower house this year but not the Senate until 2017, lower chamber Speaker Rodrigo Maia said on Wednesday.

The proposed cap is the cornerstone of Temer's strategy to plug a bulging deficit inherited from the Workers Party government of suspended President Dilma Rousseff, yet its impact on fiscal accounts will be delayed until it wins Senate approval next year.

"We must take advantage of the fiscal crisis the Workers Party left behind to show Brazilians what fiscal responsibility means," Maia told Reuters. He said the amendment will be put to a first vote in the House in the second half of October, but said Congress faced a very short legislative year due to October local elections.

Maia said he will make sure of passage this year of another piece of legislation in Temer's plan to pull Brazil from its worst recession since the 1930s - a move to allow a bigger role for private companies in developing vast off-shore oil reserves.

The bill has already cleared the Senate. It would end the obligation that corruption-hit state-led oil giant Petrobras run all new projects and pay 30 percent of the costs of subsalt developments, which the cash-strapped company cannot now afford.

Maia, who took over as speaker after Eduardo Cunha resigned last month in the face of corruption charges, said he will speed up approval of Temer's agenda for economic recovery, including a bill renegotiating the debt of Brazil's states with the federal government that will be put to the vote next Wednesday.

A Temer ally, Maia's biggest challenge will be to set a date for the chamber to vote on whether to strip Cunha of his seat, a decision he said will take place within days.

Cunha's critics demand that the discredited lawmaker be barred from politics next week. Temer's government wants a vote postponed because it could imperil his confirmation as president by the Senate, which is expected to remove Rousseff definitively from office in an impeachment trial this month.

Maia said Rousseff's conviction by the Senate for breaking budget rules to boost public spending is all but certain and her return to power out of the question. "An overwhelming majority of Brazilians don't want her back," he said.

(Reporting by Maria Carolina Marcello and Anthony Boadle; Editing by Andrew Hay)