A proposal that would give the Prince George's County government authority to tax telephone bills fell short of approval by county legislators tonight and a decision on it was delayed until later this week.

The so-called omnibus taxing proposal must get the approval of 13 members of the 25 Prince George's members of the House of Delegates, and its supporters could count only 11 votes tonight. Del. Frank J. Komenda (D) moved that the matter be postponed. The delegation discussed the controversial measure for 5 1/2 hours last Friday and another two hours tonight.

The bill would permit the county government to impose certain additional taxes now prohibited.

Royal Hart, the county government's representative in Annapolis, said County Executive Winfield M. Kelly probably would ask only for a 10 per cent tax on basic telephone rates this year. That excise tax would raise about $4 million and partially offset a projected $12.8 million deficit in the proposed county budget.

If the measure is approved in the delegation meeting later this week, it likely will sail through the legislature, as wishes of ocal delegations traditionally are not challenged by other legislators.

Prince George's is the only jurisdiction in the Washington metropolitan area that taxes neither telephone, electric or gas bills. Hart said the telephone tax would increase the average subscriber's bill by about $1 a month. The Prince George's measure would specifically prohibit local taxes on electric or gas bills.

Before considering the omnibus tax measure, the delegation voted last week to kill two bills that would have allowed the county to restructure its property tax system. These measures, proposed by Kelly at the beginning of the legislative session, would have divided tax rates into different categories permitting the county to charge different rates on apartments, homes and commercial properties.

A similar idea has now been proposed in a bill introduced on behalf of Gov. Marvin Mandel. It would among other things, create three categories for assessments, much as Kelly's plan would have created three tax rates.

But Mandel's bill would not provide the money Kelly says he needs to erase a county budget deficit this year, and, according to the county executive, would provide homeowners only a small measure of property tax relief.

Kelly has not said how much money he intends to collect through the new tax that would authorized under the measure the delegation approved tonight. He said that whatever the legislature does, a property tax increase of some size will be required.

To give homeowners some relief, the county legislative delegation voted earlier for a so-called homesteaders' bill under which persons with small incomes could receive credits against their property taxes.The delegations' support for that measure virtually assures its passage by the General Assembly.