(CNN) The Internal Revenue Service sent out the first wave of stimulus checks to Americans on Saturday, the agency said.

"#IRS deposited the first Economic Impact Payments into taxpayers' bank accounts today. We know many people are anxious to get their payments; we'll continue issuing them as fast as we can," the IRS wrote Saturday evening on Twitter

Deposits will continue in the days ahead, starting with people who have filed tax returns for 2018 or 2019 and authorized direct deposit. Others -- including people who haven't filed returns, authorized direct deposits, or receive Social Security -- will probably have to wait weeks or months before seeing their money.

The distributions are part of the $2.2 trillion economic relief package passed by Congress in March.

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