By Aidan Lewis

TUNIS (Reuters) - Allies of Libyan commander Khalifa Haftar, the dominant figure in the divided country's east, have welcomed Donald Trump's victory in the U.S. election, betting on more support for their anti-Islamist stance.

The result could boost pro-Haftar factions with strong ties to Egypt and increasingly to Russia, while diluting Western support for a U.N.-backed government in Tripoli that Haftar and his allies have opposed, analysts say.

Libya splintered into rival political and armed groupings after the uprising that toppled Muammar Gaddafi in 2011 and remains deeply divided between factions based in the east and west that backed rival governments and parliaments.

The leaders of a U.N.-backed Government of National Accord (GNA) arrived in Tripoli in March. But they have failed to fully displace the previous administration in Tripoli or win endorsement from power-brokers in the east, who accuse the GNA of being beholden to Islamist-leaning militias.

Haftar and his Libyan National Army (LNA) have been fighting a two-year military campaign against Islamists and other opponents in Benghazi and elsewhere in the east. Many suspect he seeks national power.

Haftar is aligned with the eastern parliament and government, both of which were quick to congratulate Trump on his win.

"I strongly support Trump because of his and the Republicans' resolute and decisive attitudes," said Tarek al-Jaroushi, a member of the parliament whose father commands Haftar's air force. "The Republican Party, which understands the truth about Daesh (Islamic State) and the positions and the victories of the Libyan army, will support us."

A statement from the parliament to Trump said: "We hope for your support … and we call for the lifting of the arms embargo on the Libyan army which is waging a war against terrorism."

Trump's win is likely to result in a retreat of U.S. support for the struggling GNA's leadership, or Presidential Council, said Claudia Gazzini, a Libya analyst at International Crisis Group.

"Up until now it's the U.S. Democratic administration that has been the major cheerleader of the Presidential Council, and the U.S. position on Libya has really dictated the international alignments, at least among Western countries," she said.

That could benefit Haftar, who in September seized control of key oil terminals from a rival faction aligned with the GNA.

REGIONAL POWERS

Change is unlikely in U.S. counter-terrorism policy in Libya, which has included air strikes against Islamic State in its former stronghold of Sirte, said Frederic Wehrey of the Carnegie Endowment for International Peace, but shuttle diplomacy and "the follow-on task of rebuilding Libya's government and especially security" could be reduced.

Any lessening of U.S. involvement in Libya could leave regional powers freer to act. In recent years western factions including Islamists have been close to Qatr and Turkey, whilst their eastern rivals have relied on support from Egypt and the United Arab Emirates. Haftar's allies have also cultivated ties with Russia, which printed banknotes for an eastern breakaway branch of Libya's central bank.

Trends in eastern Libya of "disengagement from party politics, a tightening of control over civil society, over mosques, over journalism" are a reflection of what is happening in Egypt, and close relations between Trump and Sisi could "strongly affect Libya", said Wehrey.

Egypt said its President Abdel Fattah al-Sisi was the first international leader to congratulate Trump by telephone. Russian President Vladimir Putin said he is ready to repair ties with the U.S. under Trump.

On Facebook, some Libyan supporters of Haftar expressed hope that a Trump victory would lead to a crackdown on Islamists in the region.

Opponents said they would fight to defend the 2011 revolution regardless. In one widely shared post a woman from the western city of Misrata wrote: "They (the LNA) may be supported by Trump, Russia, Sisi, and Haftar, but we still have God with us."

(This version of the story was refiled to correct the spelling of analyst Frederic Wehrey's name)

(Additional reporting by Ayman al-Warfalli in Benghazi and Ahmed Elumami in Tripoli; Writing by Aidan Lewis; Editing by Richard Balmforth)