By Richard Cowan and David Lawder

WASHINGTON (Reuters) - Republican leaders in the U.S. Congress on Thursday began advancing bills urgently needed to avoid federal agency shutdowns on Oct. 1 while navigating conservatives' demands to punish Planned Parenthood over an abortion controversy.

The Senate defeated Republican efforts to use a funding extension bill to cut off money to Planned Parenthood, clearing the way for a version without that provision that extends all previous funding through Dec. 11.

Senate Majority Leader Mitch McConnell of Kentucky has set the first procedural vote on that measure for Monday, two days before the federal fiscal year ends on Sept. 30.

House of Representatives Speaker John Boehner, meanwhile, laid out similar options in a closed-door meeting with Republican conservatives, who oppose any spending bill allowing federal funds to go to Planned Parenthood amid allegations that it improperly sold tissue harvested from aborted fetuses.

The nonprofit women's healthcare group has denied any wrongdoing.

Lawmakers leaving the meeting declined to say whether Boehner would defy their demands and hold a vote on a "clean" funding bill.

House Republican leadership aides said that the Ohio congressman is considering alternatives, including a separate Planned Parenthood defunding bill using special procedures to ease passage through both chambers of Congress. President Barack Obama would likely veto it.

While no final decisions were made, Representative Steve Scalise of Louisiana, a member of the House Republican leadership, told reporters: "We're going to keep attacking this (abortion) on many fronts."

He said possibilities included bills for a moratorium on Planned Parenthood funds and effectively banning late-term abortions. House Republicans will discuss the plans again on Friday morning.

Before Thursday's Senate vote, the White House warned that Obama would veto legislation to continue funding the government if it strips away federal money for Planned Parenthood, setting up the showdown with anti-abortion advocates.

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For weeks, many Republicans have vowed to punish the organization following the release of secretly taped videos in which Planned Parenthood officials discussed harvesting tissue from aborted fetuses for medical research. The group receives over $500 million in government funds annually for non-abortion activities.

Republican aides also said lawmakers were considering ramping up congressional investigations of Planned Parenthood.

The effort to defund Planned Parenthood is also being waged in states. On Thursday, the Republican-led Wisconsin Assembly approved a bill banning the state from using federal family planning money from going to Planned Parenthood and other organizations that perform abortions.

The bill needs state Senate approval and Governor Scott Walker's signature before becoming law.

(Reporting by Richard Cowan, Susan Cornwell, Susan Heavey and Brendan O'Brien in Milwaukee.; Editing by Doina Chiacu and Jonathan Oatis)