The first batch of stimulus payments promised to American taxpayers amid the coronavirus pandemic were direct deposited on Saturday, the Internal Revenue Service said.

"We know many people are anxious to get their payments; we'll continue issuing them as fast as we can," the agency tweeted Saturday evening.

On Monday, the Treasury Department said more than 80 million consumers will receive their payments this week. On social media, some Americans said they'd received payments in their bank accounts, while others said they were eagerly awaiting the checks to land in their accounts.

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Direct deposits will continue to be issued in the next couple of days to taxpayers, starting with those who filed taxes for 2018 and 2019. This includes Social Security beneficiaries who filed federal tax returns that included direct deposit information.

Individuals with disabilities, low-income workers and certain veterans who aren't typically required to file a tax return are still eligible for the Economic Impact Payments. The Treasury Department and the Internal Revenue Service announced it launched a new web tool allowing quick registration for Economic Impact Payments for those individuals.

But The Associated Press reported that some people without direct deposit information may not receive their checks until mid-August.

The agency is also launching a tracking tool called "Get My Payment" to give Americans an idea on when to expect a deposit or a check in the mail.

The cash transfers are a key part of the U.S. government's $2.2 trillion economic relief package passed in March in response to the coronavirus pandemic.

Under the economic relief package, individual taxpayers will get $1,200 each if their adjusted gross income (AGI) is less than $75,000. However, those bringing in more than $75,000 will receive less depending on their total AGI.

Married couples will receive $2,400 if they earn less than $150,000 in adjusted gross income. Taxpayers will also receive $500 for each of their children, regardless of how high their income is.

Individuals who earn more than $99,000 are phased out completely from the stimulus plan. Married couples earning more than $198,000 (and no kids as dependents) also aren't eligible for payments.

According to the bill, immigrants qualify for a stimulus check if they have a valid Social Security number. Those with green cards or certain work visas are eligible for a check, but non-resident aliens, temporary workers and immigrants in the country illegally are not.