Some of those who are being asked to return were laid off by mistake, according to two sources.
Others were let go before management realised that their work and experience may be necessary to build the new features Mr Musk envisions, the sources said.
Twitter cut close to 3,700 people this week via email as a way to trim costs after Mr Musk’s acquisition, which closed in late October.
Many employees learnt they had lost their job after their access to company-wide systems, such as email and Slack, was suddenly suspended.
The requests for employees to return demonstrates how rushed and chaotic the process was.
A Twitter representative did not reply to a request for comment. Twitter’s plan to hire back workers was previously reported by Platformer.
“Regarding Twitter’s reduction in force, unfortunately there is no choice when the company is losing over $4M/day,” Musk tweeted on Friday.
Twitter has close to 3,700 employees remaining, according to the sources.
Mr Musk is pushing those who remain at the company to move quickly in shipping new features, and in some cases, employees have even slept at the office to meet new deadlines.
Twitter unveiled a new Twitter Blue subscription plan at the weekend, offering a verification check mark for any user who pays $8 a month.
The company also said it would soon be launching other features, including half the advertisements, the ability to post longer videos and get priority ranking in replies, mentions and searches.