Democratic Senator Mark Warner said the briefings were "deeply disappointing".
The social giant Facebook has shared some information about Russian linked accounts with Google.
Google is investigating the extent to which Russian actors spread misinformation through the platform's websites.
Facebook has already handed copies of the ads and information about the relevant accounts over to Special Counsel Robert Mueller, who is conducting an investigation into Russian meddling in the 2016 election.
Russian Federation has denied meddling in the election.
Twitter made the announcement as it briefed members of the U.S. government behind closed doors.
The statement added that RT, which was named in January in a United States intelligence report on election interference, spent at least $274,100 in 2016 for 1,823 tweet ads or "promotions" that "definitely or potentially targeted the USA market".
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Those accounts did not support any particular candidate, but instead posted inflammatory information on hot topics such as immigration. The Post reported last week that ads promoting the group Black Lives Matter, for example, were targeted toward people who lived in Ferguson, Mo., and Baltimore, two cities that have seen large protests against the police shootings of unarmed black people and have recruited members of Black Lives Matter. Notably, it also added that it has found 179 additional accounts which violated its rules. The company said that its automated systems catch more than 3.2 million suspicious accounts globally per week, which is more than double the amount the company detected this time past year.
Facebook CEO Mark Zuckerberg said recently that the company will provide congressional investigators with the contents of the 3,000 ads bought by a Russian agency, and he pledged to make political advertising on its platform more transparent.
In a statement, RT mocked the notion that its almost 2,000 ads on the social network in 2016 were any different from what other media groups were doing.
As with the Facebook accounts, the Twitter accounts sought to amplify political discord by highlighting hot-button political issues like race and immigration. Both the House and Senate intelligence panels are inviting Twitter, Facebook and Google to testify this fall.
Warner said the information Twitter shared "was frankly inadequate on nearly every level". Cybersecurity firm FireEye Inc. discovered thousands of fake accounts linked to Russian Federation that regularly posted anti-Clinton messages.
"This is an ongoing process and we will continue to collaborate with investigators", the company said in its statement.
A spokesperson for Warner said that he's interested in the activity of the social media accounts through which the ads were purchased. They asked not to be identified discussing a private investigation. "And there will always be tools or methods we can not talk about, because doing so would only help bad actors circumvent them", the company said.