The refunds are for people who collected unemployment last year and filed their 2020 returns before mid-March.
The newest round of refunds has already gone out as direct deposits. Paper checks will be sent starting Friday.
The average refund for overpayment is about $1,200.
Meanwhile, the Biden administration is beginning to distribute expanded child tax credit payments, giving parents on average $423 this month, with payments continuing through the end of the year.
President Joe Biden increased the size of the tax credit as part of his $1.9 trillion coronavirus relief package, as well as making it fully available to families without any tax obligations. The benefit is set to expire after a year, but Biden is pushing for it to be extended through 2025 and ultimately made permanent.
The Associated Press contributed to this report.