* Israeli PM accused of backing Romney over Obama
* Netanyahu denies that, says US alliance is firm
* Faces election in January, tipped to win
JERUSALEM, Nov 8 (Reuters) - Benjamin Netanyahu phoned Barack Obama to congratulate him on his re-election on Thursday, after critics accused the Israeli prime minister of backing Mitt Romney and jeopardising ties with Washington.
Relations between Netanyahu and Obama have long been testy, mainly over how to deal with Iran's nuclear programme.
After Obama's re-election on Tuesday, some of Netanyahu's opponents - who hope to defeat him in an election on Jan. 22 - accused the right-wing leader of backing the wrong man.
Netanyahu's office said he had phoned Obama, saying of the election: "It was a vote of confidence in your leadership."
Netanyahu said he "looked forward to continuing to work with the president to address the great challenges facing the United States and Israel and to advance peace and security in our region," a statement said.
In a speech earlier in the day, Netanyahu said some of his critics "were trying to cause conflict between us and the United States" by alleging he had shown preference for the Republican challenger.
"They won't get away with it," he said, in remarks that appeared to be aimed mostly at Ehud Olmert, the former prime minister who is considering running in the upcoming election, which polls predict Netanyahu will win.
"The alliance with the United States is firm," Netanyahu said.
Israeli media quoted Olmert, former head of the centrist Kadima party, as telling a meeting of U.S. Jewish leaders in New York on Wednesday that Netanyahu had intervened in American politics and might not have a friend in the White House.
Financial backing for Romney from a U.S. casino magnate who is also one of Netanyahu's biggest supporters was cited by critics as evidence he had tried to undermine Obama. Netanyahu denies having shown any preference during the U.S. campaign.
"We have a strategic partnership (with the United States), but most of all in security, where the cooperation is deep, wide and solid," Netanyahu said. (Writing by Jeffrey Heller; Editing by Robin Pomeroy)