A committee of federal agencies declared yesterday 56 Virginia countries and 23 cities eligible for several loan and grant programs to help them increase water supplies in their communities.

Arlington, Faifax, Loudoun, Prince William, Stafford and Fauquier counties and Alexandria, Fairfax City and Falls Church are among the jurisdictions eligible for the aid announced by the Interagency Drought Emergency Coordinating Committee.

Donald Carbone, disaster program officer for the Federal Disaster Assistance Administration, said the Virginia communities will be eligible for funds to relieve problems caused by water shortages, and for low-interest emergency assistance grants and loans.

Farmers can apply for 5 per cent loans from the Farmers Home Administration to covr prospective crop and livestock losses, and businessmen affected by the drought are eligible for loans to cover their losses, Carbone said.

Virginia Gov. Mills E. Godwin asked the coordinating committee last week to declare 78 counties and 35 cities eligible for the assistance, Carbone said. The governor also has asked President Carter to declare 33 Virginia counties as disaster areas because of the effect of the drought on the farmers.

A spokesman for the governor said yesterday that the White House has made no declaration yet. If it does so, Virginia's farmers will be eligible for several additional programs that can aid them in fighting the state's most severe drought since 1930.

Henry B. Jenkins, a federal Economic Development Administration spokesman, stressed that the grants and loans available from his agency are strictly to support short-term drought relief.

The grants and loans from the development agency are available for communities with a population of 10,000 or more. Of the $175 million appropriated for the program by Congress this year, $12 million already had been used to help California jurisdictions, while other money has been used to help Northwest states.

Jenkins said the funds are used for the improvement, expansion or construction of water supply systems, to purchase and transport water to provide immediate relief from the drought, and for water consumption.