The head of the US capital's council introduced a resolution to give the city's blessing to calls by lawmakers and activists to rechristen the street after the Nobel laureate in hopes of freeing him.
But Phil Mendelson's resolution said that the federal and not the local government had jurisdiction over International Place, where China and several other nations have built embassies.
He called for a vote by the US Congress, where the proposal enjoys support across party lines.
Similar action in support of Liu "would send a clear and powerful message that the United States remains vigilant and resolute in its commitment to safeguard human rights around the globe, particularly at a time when the world community remembers the events of Tiananmen Square 25 years ago this month," the draft resolution said, referring to the deadly crackdown on pro-democracy student demonstrations.
Liu won the Nobel Peace Prize a year later, leading China to censor any mention of the award and to put his wife under house arrest.
After US lawmakers proposed the street renaming several weeks ago, a Chinese foreign ministry spokesman warned it would be a "provocative action" and called Liu "a man who has violated Chinese laws.