As Agrawal took questions on Thursday from staff that were posted on the company's Slack messaging service, he encouraged employees to remain focused and told them "we as employees control what happens," said the source, who did not want to be identified because they were not authorised to speak publicly on the matter.
The meeting came after news broke that the Tesla chief executive officer had offered to buy the social media company for $US43 billion ($A58 billion).
Agrawal told staff that the board was continuing to review Musk's offer, but that he was limited in what he could share with the employees.
In one section of the question and answer session, one employee asked how the company arrived to the decision to offer Musk a board seat.
"Are we just going to start inviting any and all billionaires to the board?" according to a section of the meeting heard by Reuters.
Agrawal responded that the board was acting in the best interest of shareholders.
"I have a strong point of view that people who are critical of our service, their voice is something that we must emphasise so that we can learn and get better," he said.
Another employee submitted a question asking Agrawal to address how he viewed Musk's definition of free speech and whether it aligned with how Twitter approaches the concept.
Agrawal did not directly address the question, saying much of the company's work was focused on continuously improving "the health of conversation" on Twitter.
Earlier in the Q&A, Agrawal said he believed "Twitter stands for way more than one human, any human."
A Twitter spokesman declined to comment on the meeting.