Chrysler Corp. made a profit in October, its first profitable month in two years, according to Chairman Lee A. Iacocca, who urged Chrysler's dealers to continue taking the company's cars despite their concerns over high interest rates and slow auto sales.

Iacocca mentioned the October profit in an interview with the industry weekly Automotive News, which was published yesterday. "We should have run up a flag and thrown a big party," Iacocca told the trade journal.

He didn't give any details, however. Chrysler, like other major companies, reports financial results every three months.

Despite the good news, Iacocca said he doubted Chrysler, could show a profit for the October-to-December period if interest rates remain high and sales continue at current depressed levels.

Chrysler's success in October could mean disappointing results this month and next, unless the economy improves, lifting car sales. Chrysler, like other automakers, considers a car to be "sold" when it is shipped to a dealer. At that point, the dealer owns the car and is obliged to pay Chrysler for it.

If dealers have too many unsold "October" cars, they will be less willing to accept delivery of Chrysler's production now and in the future, auto analysts note.

"Our biggest problem is getting the dealers to take the three weeks of December production. It all hinges on that," Iacocca told the trade journal.

"If sales continue the way they are the last 10 days, I doubt if the quarter will be profitable," he said.

"I have a feeling we are headed into solid concrete with some dealers and fleets telling us to delay the units they have ordered. Our only problem now is interest rates," he added.

Chrysler's sales for the first 10 days of November were 19 percent higher than sales in the same period a year ago, but the company's sales then had been extremely low. By comparison, the November 1980 figure is 34 percent below the sales figure for the identical period two years ago.

The effects of high interest rates and depressed car sales have been particularly painful for Chrysler's new line of 1981 K cars, the front-wheel-drive compacts Chrysler is counting on to lead its recovery back to profitability.

Handicapped as well by some production and distribution problems, K cars are currently selling well below the sales target set out in Chrysler's financial recovery plan. Chrysler recently has increased production of lower-priced models to boost K-car sales.

In the interview, Iacocca also confirmed that Chrysler had been privately discussing a possible joint manufacturing arrangement with Volkswagen last year when word of the talks became public. Volkswagen then backed away, Iacocca said.

VW decided then that "it was not a good time to get involved in view of Chrysler's mounting losses," Iacocca said. A June 21, 1979, report in Automotive News had said that Chrysler and Volkswagen were negotiating a potential merger, and both companies issued denials at that time. Iacocca said that the report had been overstated.