The Internal Revenue Service yesterday issued withholding regulations designed to halt taxpayer cheating on interest and dividend payments.

Starting next July, under legislation Congress approved last summer at the urging of the Reagan administration, organizations such as banks, brokerages and corporations will be required to withhold 10 percent of all interest and dividend payments to the nation's savers and investors.

Low-income and many elderly taxpayers will be exempt from the new withholding law, provided they file for an exemption at each institution where they have an account. Under the rules issued yesterday, organizations making the interest or dividend payments will have the option of giving these taxpayers a blanket exemption or requiring them to file a separate request for every account they hold.

Banks, savings and loan associations and credit unions will not be required to withhold taxes on any account that does not receive $150 in interest each year.

Most financial institutions fought the withholding law earlier this year in Congress and yesterday the president of the American Bankers Association urged his group's 14,000 member organizations to enlist their support in mobilizing stockholders and depositors to fight for repeal of the law.

To pay for the administrative costs of starting up the new withholding program, the IRS will allow financial institutions during the first year of the program to use the money withheld from customers for 30 days before they have to send it to the government. This amounts to an interest-free loan on billions of taxpayer dollars. Banking industry officials estimate the startup costs at $1.5 billion.

In 1980, the last year for which statistics are available, the IRS said U.S. taxpayers collected $38 billion in dividends and $101 billion in interest. Because of the various exemptions in the law, not all of that amount would have been subject to withholding.

As a result of the new withholding program, the Treasury Department said it expects to collect an additional $1.34 billion in fiscal 1983 and $5.25 billion in fiscal 1984. Although institutions already are required to report payments to the government, that information often slips by the IRS unless the taxpayer reports it.

The new rules do not increase the amount of tax owed, but it allows the government to get its hands on some of the money owed on interest and dividends early. The federal government has been withholding income taxes from employe paychecks since 1943.

The IRS said it also is working on new rules that will require stockbrokers to report on the activities of their customers, so the agency can get a better fix on what gains taxpayers are likely to have realized on stocks, bonds, and commodities trades.

IRS Commissioner Roscoe L. Egger told reporters yesterday that the IRS "leaned over backwards" to accommodate the financial industry's complaints about the potential administrative burdens of the new law. "The regulations have accommodated just about every major problem" brought to the agency's attention by the financial industry, Egger said.

A spokesman for the bankers group said that "at first glance" it appears the IRS did "favorably" act on most of the financial industry's complaints, but said even the accommodative stance of the regulation writers "doesn't make the whole idea of withholding interest and dividend payments any less onerous."

The complicated rules, on which the IRS must now hold public hearings, exempt individuals who owe the government less than $600 in taxes and couples that pay less than $1,000. Individuals over age 65 who pay less than $1,500 in taxes and elderly couples who pay less than $2,500 also are exempt.

The IRS will publish exemption certificates, but any institution is free to design its own and require depositors to use its forms.

On so-called NOW accounts -- checking accounts that pay interest -- and passbook savings accounts, a bank can choose to withhold interest either when it is paid or at the end of the year. All other interest and dividend payments must be withheld when they are paid or credited to the taxpayer.

If a bank account earns less than $150 in interest, the depository institution does not have to withhold taxes. If the bank chooses to pay interest once a year, its decision whether it needs to withhold or not is simple.

But for a bank that chooses to withhold taxes at the time it credits the interest to passbook and NOW accounts and for all other interest-bearing accounts, the institution must decide if the interest payment, at an annualized rate, works out to $150 or more. For example, if a bank pays quarterly interest of $40 on March 31, that is equivalent to an annual payment of $160. The bank will withhold $4 from the customer's payment and remit it to the government. If the next interest payment drops to $35, the bank would not be required to withhold.