WASHINGTON—Trump lawyer Rudy Giuliani said the president had repaid his longtime attorney, Michael Cohen, for a $130,000 payment Mr. Cohen made to a former adult film star in October 2016 in exchange for her silence about an alleged sexual encounter.

Mr. Giuliani, who joined the legal team representing President Donald Trump in the Russia investigation last month, told The Wall Street Journal Wednesday evening that the president had repaid Mr. Cohen, but he suggested that Mr. Cohen made the payment without Mr. Trump’s knowledge...