WASHINGTON—President Trump accused Google of elevating critical news stories about his presidency at the expense of friendly conservative voices, signaling potential government action if it didn’t change its alleged practices.

Mr. Trump complained Tuesday on Twitter that Google search results for the words “Trump news” returned results primarily from what he labeled “Left-Wing Media.” Google and others “are suppressing voices of Conservatives and hiding information and news that is good,” he wrote. He said the way such sites...