NSA director Admiral Michael Rogers made the comments at a congressional hearing in response to Senator John McCain's criticism of Twitter for refusing access to a real-time analytics service called Dataminr.
McCain queried Rogers about a Wall Street Journal report in May that Twitter had blocked intelligence agencies from using Dataminr, which uses algorithms and location tools to reveal patterns among tweets.
The veteran senator said the report indicated that Dataminr had alerted its clients minutes before this year's Brussels attacks and at the time the November Paris attacks began to unfold.
Rogers replied: "Yes sir, and at the same time (Twitter is) still willing to provide that information to others for business, for sale, for revenue."
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He added, "I'm perplexed by their approach in this particular incident.. Clearly, I wish I had a better understanding, and perhaps there are insights that I am not aware of."
Twitter has said it allows both government and business to use the data, as long as it is not for "surveillance" purposes.
Media reports have said that Twitter, which owns a stake in Dataminr, did not want to appear to be too close to US intelligence.
"Dataminr uses public tweets to sell breaking news alerts to media organizations and government agencies, for non-surveillance purposes," a Twitter spokesman said in a statement.
"Due to privacy concerns, we have not authorized Dataminr or any third party to sell data to a government or intelligence agency for surveillance purposes. This is a longstanding Twitter policy, not a new development."
The statement added that Twitter "responds to valid legal process issued in compliance with applicable law, and our most recent transparency report shows over 5,000 US government information requests in 2015 alone.