By Luc Cohen and Matt Spetalnick

CARACAS/WASHINGTON, Sept 19 (Reuters) - Venezuela's rival political factions will take their power struggle to New York next week, where representatives of President Nicolas Maduro and opposition chief Juan Guaido will each try to convince a gathering of world leaders at the United Nations that their boss is the country's legitimate head of state.

The United States and more than 50 other countries recognize Guaido, the leader of the opposition-controlled National Assembly, as the rightful president. Guaido in January invoked the constitution to assume a rival presidency to Maduro, arguing the socialist president's May 2018 re-election was a sham.

But the 193-member U.N. General Assembly still recognizes Maduro, who retains the support of the U.N. Security Council's veto-wielding permanent members Russia and China, setting the stage for the two sides to air their public grievances as they battle for international backing.

A round of negotiations brokered by Norway in recent months, aimed at peacefully resolving the crisis, has failed.

Guaido is seeking to get more countries, especially the European Union, to implement sanctions on Venezuela, as the United States has done.

Maduro, who has overseen a collapse of the OPEC nation's once-prosperous economy and has been accused by the U.N.'s High Commissioner for Human Rights of rights violations, wants to heap pressure on the United States to lift sanctions on state oil company PDVSA and members of his inner circle.

Critics say his government's decisions this week to free a jailed opposition lawmaker and reform Venezuela's electoral body, long accused of bias, were aimed at improving Maduro's image before the U.N. gathering.

"They want to use the U.N. meeting to wash their face, because they are not reaching any real solutions for the Venezuelan people," Carlos Valero, an opposition lawmaker who sits on the National Assembly's foreign affairs committee, said in an interview on Wednesday.

Maduro calls Guaido a U.S. puppet seeking to oust him in a coup, and blames Washington's sanctions for Venezuela's economic woes. Maduro himself said he will not attend the U.N. gathering, but he tasked two cabinet members with presenting a petition condemning the sanctions to Secretary General Antonio Guterres.

"The U.N. Secretary General and all the U.N. agencies should raise their voice to condemn the aggression Venezuela is being subjected to, to condemn the illegal blockade," Foreign Minister Jorge Arreaza told reporters in Geneva last Friday. "We believe that a lot more can be done from the United Nations."

'UNTIL MADURO IS GONE'

Guaido has not yet decided whether he will attend, according to his U.S. envoy Carlos Vecchio. Julio Borges, an exiled opposition lawmaker recently named Guaido's chief diplomat, will be in New York for side events aimed at spotlighting Venezuela's humanitarian crisis and Maduro's alleged support for armed rebels in Colombia.

The events include a likely meeting of the signatories of the Rio Treaty, invoked earlier this month by a dozen members of the Organization of American States (OAS), including the United States. The treaty is a Cold War-era mutual defense pact that the countries said they had invoked in response to what they called Maduro's threat to regional stability. The OAS, unlike the U.N., recognizes Guaido as Venezuela's rightful leader.

Maduro's government denies supporting the Colombian rebels and says the Rio Treaty is a precursor to military intervention.

In April, U.S. Vice President Mike Pence called on the U.N. to revoke the credentials of Maduro's government and recognize Guaido, but Washington has taken no action to push the measure at the General Assembly. Diplomats said it was unlikely Washington would get the support needed.

Both Washington and Venezuela's opposition are seeking to counter perceptions that their efforts to oust Maduro have stalled.

Though differences over Iran and Afghanistan policy were the main reasons for U.S. President Donald Trump's firing of his hawkish national security adviser John Bolton last week, Trump had also grown increasingly impatient with the failure of sanctions and diplomatic pressure to push Maduro from power.

Despite Trump's vows that all options were on the table, he had resisted Bolton's push for more military planning, according to a person familiar with the matter. Trump's aides have made clear that he is likely to impose further sanctions but the economic weapons at Washington's disposal appear to be dwindling.

U.S. State Department spokeswoman Morgan Ortagus said in a statement on Tuesday that the United States continued to stand with Guaido and that sanctions "will not be lifted until Maduro is gone."

"We look forward to coming together with regional partners to discuss the multilateral economic and political options we can employ to the threat to the security of the region that Maduro represents," she said. (Reporting by Luc Cohen in Caracas and Matt Spetalnick in Washington, Additional reporting by Stephanie Nebehay in Geneva and Michelle Nichols in New York, Editing by Rosalba O'Brien)