Ending a week of speculation about its future, Auto-Train Corp. announced yesterday that the Seaboard Coast Line Railroad has agreed to a new financing plan that will keep the Auto-Train running.

At the same, Auto-Train announced it lost $223,000 (14 cents per share) in the three months ended June 30, down sharply from the $668,000 (35 cents) loss a year earlier.

The announcement, which also included several other details of Auto Train's financial problems, will allow trading of the company's shares to resume Monday on the American Stock Exchange. Trading was halted a week ago at the company's request.

But Amex has notified the Washington railroad that its stock may be taken off the listings because it no longer meets the exchange's financial guidelines. Amex rules provide for delisting a stock when the company loses money for three straight years and its net worth fails below specified levels.

The company said its annual shareholders meeting, which was adjourned two weeks ago, will be convened on Monday at 2 p.m. at the Twin Bridges Marriott in Arlington.

Yesterday's announcement said Auto-Train's future still depends on the company's ability to raise at least $3 million in new capital and to refinance a $3 million bank loan that is overdue.

If those conditions and others are met by the end of the year, the Seaboard Coast Line has agreed to cut by 20 percent the amount it charges for providing the tracks and train crews to haul the Auto-Train to Florida.

Auto-Train owes the Seaboard $1.1 million in overdue operating charges this year and another $1.1 million from last year. Yesterday's announcement disclosed for the first time that Seaboard had demanded payment and threatened to terminate its agreement to operate the train, which would have ended Auto-Train service.

Seaboard withdrew that demand, Auto-train said, and agreed to cut the operating charges by one-fifth for two years starting in April of this year. That will cut Auto-Train's expenses by about $1 million a year.

To qualify for that savings, however, Auto-Train must pay off its 1979 debts to Seaboard this year and pay its 1978 bills in monthly installments starting next January, as well as obtain new financing.

Yesterday's announcement revealed Auto-Train has changed its plans for raising new money and now hopes to make a public offering for 1.5 million new shares of common stock plus warrants to buy another 1.5 million new shares.

Previously, the company said it planned to try to sell 800,000 shares of convertible preferred stock.

Sale of the additional common stock does not require the approval of Auto-Train shareholders.

The preferred stock issue would have required shareholders' okay; the company failed to get that approval at the annual meeting two weeks ago.

Auto-Train also confirmed a report in The Washington Post this week that it had withdrawn its application for a $3 million loan guarantee from the Economic Development Administration of the Department of Commerce, after EDA rescinded its tentative committment to give the guarantee.

The railroad said EDA withdrew the offer because of delays in starting a new auto-train service between Newark, N.J., and Florida. Extension of the northern terminus of the Auto-Train route to Newark from Lorton, Va. will come no earlier than the fall of 1980, the company now says.

Auto-Train's report on operations for its latest three-month period showed the company's revenues increased to $6.8 million from $6.2 million a year ago.Ticket prices this year are lower than last year, indicating the number of people and cars traveling by Auto-Train is up.

If the reduction in operating charges offered by the Seaboard is put into effect, Auto-Train said it would restate its quarterly results to show a $30,000 profit.