NEW YORK (Reuters) - A New York state judge on Tuesday said Smartmatic can pursue part of its lawsuit claiming that Fox News Network, Rudolph Giuliani, and others falsely accused the electronic voting systems maker of helping rig the 2020 U.S. presidential election to favor Democrat Joe Biden.

Justice David Cohen of the state supreme court in Manhattan rejected Fox's bid to dismiss claims, and dismissed some but not all claims against Giuliani, who worked as a lawyer for Republican President Donald Trump.

Cohen also refused to dismiss claims against Fox host Maria Bartiromo and former Fox host Lou Dobbs. He dismissed claims against Fox host Jeanine Pirro and former Trump lawyer Sidney Powell.

(Reporting by Jonathan Stempel in New York; Editing by Chris Reese)