Mayor Marion Barry signed a bill yesterday that grants delayed tax relief to the District's banks and savings and loan associations. The measure now goes to Capital Hill. Without opposition from Congress, it will become law in 30 days.

Under the Financial Instructions Tax Act of 1980, banks and thrifts will be taxed on the basis of net, rather than a gross income. Instead of a gross ernings tax of 5 to 6 percent on banks and 2 percent on savings and loans, financial institutions will hereafter pay a franchise tax of 9.9 percent on net income. They will also be subject to personal property taxes of $2.83 per $100 on equipment and the like.

The change, long sought by the beneficiaries, will put them on the same tax basis as other non-financial bsuiness in the District and banks in other states. Under the present system banks and thrifts have to pay taxes on their gross earnings even though they incur net losses. For example it is estimated that D.C. savings and loans will have to pay $8.1 million in taxes this year while suffering losses of $7.4 million.

In return for eventual relief, the banks and thrifts grudgingly accepted a three-year phase-in of the new system. This means, in effect, that they will pay higher taxes in the short run.

During fiscal 1981 the District government will recieve an additional $3.6 million in revenues from these institutions. In the second year the amount would be reduced to $554,000. After that the relief would result in revenue losses to the District of $2 million the first year, and $7.2 million by 1985. l