With Democrats boycotting the hearing, the Republican-controlled Senate Judiciary Committee voted to authorise the legal orders if Facebook’s Mark Zuckerberg and Twitter’s Jack Dorsey did not agree to testify voluntarily.
The committee wants to hear from them about “the suppression and/or censorship of two news articles from the New York Post”, according to the subpoena document.
Senators also want information from the executives about their companies’ policies for moderating content “that may interfere” with federal elections.
Representatives of Facebook and Twitter declined to comment.
The urgency increased on Thursday as US officials said Russian hackers have targeted the networks of dozens of state and local governments in recent days, stealing data from at least two servers.
The revelation was certain to stoke fears that Americans’ confidence in the upcoming election’s results could be undermined.
Russia backed Donald Trump’s 2016 campaign through hacking of Democratic emails and a covert social media campaign, with Facebook becoming an unwitting conduit for misinformation and election disruption.
Facebook and Twitter acted last week to limit the online dissemination and sharing of an unverified political story from the conservative-leaning New York Post that targeted Democratic presidential nominee Joe Biden.
The story, which other publications have not confirmed, cited unverified emails from Mr Biden’s son Hunter that were reportedly disclosed by Mr Trump’s allies.
One email purported to show a top adviser for Burisma, the Ukraine gas company where Hunter Biden held a board seat, thanking the younger Biden for giving him an opportunity to meet the elder Biden, who was vice president at the time.
Mr Trump’s campaign seized on the report, though the account raised more questions than answers, including whether emails at the center of the story were hacked or fabricated. The FBI is investigating whether the emails are part of a foreign influence operation.
It was the first time in recent memory that the two social media platforms enforced rules against misinformation on a story from a mainstream media publication.