US Senator Marco Rubio, the bill's sponsor, and Senate Foreign Relations Committee chairman Jim Risch, started the quick passage process on Thursday in a bid to speed up the passing of the bill, which would clear the way for sanctions against individuals deemed to have violated Hong Kong's autonomy from mainland China, reports the South China Morning Post.
The strategic procedure carried out by the Senate's leadership checks for last-minute opposition to bringing a bill immediately to the floor for a vote.
If no senators voice opposition to side-stepping a formal vote, the bill will pass.
However, Rubio and Risch were not able to clinch passage by the end of the Senate session on Thursday, according to one Senate foreign relations committee aide.
"Sometimes the hotline process takes more than a day, so it's still moving along," the South China Morning Post quoted the aide as saying, adding that the floor was closed until November 18.
Earlier in the day, Rubio urged the Senate to immediately pass the legislation.
"The world witnesses the people of Hong Kong standing up every day to defend their long-cherished freedoms against an increasingly aggressive Beijing and Hong Kong government.
"Now more than ever, the United States must send a clear message to Beijing that the free world stands with Hongkongers in their struggle," the Florida Republican added.
Hong Kong has increasingly has become a battleground between police and protesters since June, when mass peaceful marches targeted a government proposal, since shelved, to allow the city's criminal suspects to be extradited to mainland China.
Those protests have since morphed into a larger activism, with citizens demanding the right to vote for their own city leaders.
This week, the pro-democracy protests have taken a dark turn. On Wednesday, a 15-year-old boy was hit in the head by what appeared to be a tear-gas canister, according to the city Hospital Authority.
A day earlier, a battle between police and protesters turned a top university's campus into a combat zone.
On Monday, a Hong Kong police officer shot a protester, while in a separate incident, protesters apparently set on fire a man who had expressed support for police outside an MTR station.
( With inputs from IANS )