Savings and loan companies based in McLean and Petersburg announced plans yesterday to merge into a single institution with $600 million of assets and 35 offices from the Potomac River to the North Carolina border.

If approved by stockholders and regulatory agencies, First Financial of Virginia Corp. of McLean would combine with Virginia First S&L of Petersburg to become the largest savings and loan business in Virginia.

First Financial is the holding company for Washington-Lee S&L, which has assets of $368 million and 23 offices, located mostly throughout Northern Virginia.

Both institutions are strong, with reserve funds and net worths well within regulatory guidelines at a time when many S&L institutions have faced unprofitable operations because of the cost of money in terms of interest they must pay. Some forced mergers of weak S&Ls are expected because of this environment.

The agreement approved by directors and announced yesterday requires stockholders of the McLean firm to approve a reduction in the par value of their shares to $2.50 from $5 as well as authorization for 2.5 million new shares. Directors said that after this authorization, they will split the stock 2 for 1, thus creating 947,030 shares outstanding before the merger.

At the time of the merger, Virginia First owners will receive about 1.25 shares of the McLean firm for each share of their company owned; there are 1.085 million shares now outstanding.