Mayor Marion Barry asked the City Council yesterday to give an estimated 10,000 District of Columbia taxpayers another chance to qualify this year for homeowner's exemptions that would reduce the tax bills on their homes.

The taxpayers affected either failed to file affidavits claiming the tax benefits, or their affidavits were lost or improperly processed by the city, Barry said. As a result, he said, city offices have been swamped by hundreds of protesting telephone calls and letters.

Under legislation proposed by the mayor, the affected real estate taxpayers would still be required to pay the higher bills they already have received for the first installment, due Sept. 17. They would be given credit through lower bills for the second installment next spring.

"This . . . is the maximum response that we can possibly make" to provide fair treatment to the taxpayers, Barry said in a message to the council.

Barry proposed that taxpayers be given until Nov. 30 to file affidavits. He asked the council to invoke emergency powers-- possibly at its next meeting on Tuesday-- to pass the bill, which would become law immediately upon being signed by the mayor.

The mayor also said he plans to propose legislation soon that would do away entirely with the requirement in future years that homeowners file affidavits to receive the benefit of residential tax rates.

"The least likely to respond to bureaucratic forms, such as the affidavit in question," the mayor declared, "are the low-income, the handicapped, the elderly, those out of town during the affidavit-filing period and those who purchased their homes after the filing deadline has passed. These people should not be penalized . . . "

The deadline this year was July 2.

The affidavits, introduced in 1977, grant homeowners an exemption from taxation on the first $9,000 in assessed valuation on the homes they occupy.

This year, for the first time, the affidavits were needed to qualify for taxation at the rate of $1.22 per $100 of assessed valuation provided by law for owner-occupied homes.

If no affidavit was filed, the taxes were billed at the rate of $1.54 per$100 of valuation established for residential rental properties. The council also voted a higher rate, $1.83 per $100, for commercial properties.

The owner of a dwelling assessed at the city average of $60,000 this year would save $139 by filing the affidavit.

When taxpayers began complaining last month about tax bills they regarded as too high, the city's Finance and Revenue Department put most of the blame on taxpayers for failing to file the forms. But it acknowledged that the department may have made mistakes, too.

Barry said taxpayers who have contacted the city gave many reasons why the forms were not on file. "Among [these] are improper processing by the [finance department] or poor mail delivery. . . It is difficult to argue with such claims, since we have no way of proving one way or the other" who is to blame, the mayor declared.