The company sought to send its senior vice-president for global affairs, Kent Walker, but was rebuffed.
Dorsey offered an explanation of how San Francisco-based Twitter uses "behavioral signals", such as the way accounts interact and behave on the service.
Both Dorsey and Facebook's Chief Operating Officer Sheryl Sandberg have confirmed they will be in Washington for the Senate hearing September 5. Either Google CEO Sundar Pichai or Alphabet CEO Larry Page were supposed to attend the hearing. That scrutiny has led to additional criticism over the companies' respect for user privacy and whether conservatives are being censored.
"Any suggestion that Jack made or overruled any of these decisions is completely and totally false", Twitter's chief legal officer, Vijaya Gadde, said in a statement.
This will be the first time Sandberg has publicly faced significant questioning about Facebook's role in the 2016 election.
Lula da Silva barred from running for Brazil's presidency
But he is adored by millions of Brazilians due to the prosperity Brazil enjoyed under his leadership from 2003 to 2010. Lula's social media followers remain upbeat, though.
Dorsey will follow the Senate hearing with another hearing that could be politically more contentious - an appearance before the House Energy and Commerce Committee that will specifically address Twitter's "algorithms and content moderation".
President Donald Trump used Twitter on July 26 to fault the website, without evidence, for using so-called shadow banning, or limiting the visibility of, prominent Republicans. Twitter denies that's happening.
The Menlo Park, California-based company revealed past year that a Russian internet agency had used the platform to try to influence the 2016 USA presidential election. While Burr said he believes Facebook and Twitter do understand the problem, it took both companies several months previous year to acknowledge they had been manipulated.
In prepared testimony released by Facebook Tuesday, Sandberg said that Facebook was "too slow to spot" Russia's purported influence operation and "too slow to act". Thirteen Russians were indicted by special counsel Robert Mueller earlier this year on charges of an elaborate plot to disrupt the 2016 US presidential election by creating fake accounts that pushed divisive issues on social media.