Cities Service Corp., which put itself up for sale a week ago after the collapse of a merger offer from Gulf Oil Corp., last night turned down a $3.8 billion takeover bid from Occidental Petroleum Corp. -- but left the door open for Occidental to increase its offer.

The announcement, which came after Cities' board met for 3 1/2 hours in in New York, also left open the possibility that Cities might find another buyer for all or part of the company.

"Your proposal would not meet the board's objective of maximizing value for Cities Service shareholders," Cities Chairman Charles J. Waidelich wrote Occidental Chairman Armand Hammer in a letter delivered after the meeting, which ended about 8 p.m. "While willing to explore with you a possible review of your proposal, we intend to continue discussions with various other companies."

Occidental, which made its offer last Friday and demanded a response from Cities by yesterday, had no immediate comment on the Cities board's action.

Officials of Tulsa, Okla.-based Cities embarked on a frantic search for a buyer last week after Gulf withdrew its $4.8 billion offer, and they threatened to liquidate their company if they could not find a suitable merger partner. Although several other companies have been mentioned in recent days as potential suitors, Occidental was the first to venture a concrete offer.

A Cities spokesman said last night that "there are very serious discussions going on" with other companies regarding a sale of all or part of Cities Service. He would not elaborate.

Cities is the nation's 19th-largest oil company and Occidental is ranked 12th. A merger of the two would create a company ranking eighth among the nation's oil companies and 12th among industrial concerns.

In its bid, Occidental offered to pay $50 in cash for 38.2 million Cities share, about half the outstanding stock in the company. Occidental then would offer a package of securites for the remaining stock. Financial experts said it was difficult to fix the value of the zero-coupon bonds and preferred stock being offered by Occidental in the second stage of the offer, but they estimated it to be around $50 per Cities share.

That price was considerably below the $63 a share that Gulf had offered. Many analysts believed that Gulf offered too much, and some believe that the Pittsburgh-based company pulled out of the deal because it had second thoughts about its offering price. Gulf said it withdrew its offer because of antitrust objection raised by the Federal Trade Commission, but Cities has filed a $3 billion breach-of-contract suit against Gulf. Several Cities stockholders also have sued Gulf.

Occidental's $50-a-share offer would have come close to bailing out Wall Street professionals and other speculators who purchased high-priced Cities stock in expectation of receiving $63 a share from Gulf, only to see the value of the stock fall to less than half that when Gulf withdrew its offer. Wall Street sources say the speculators purchased Cities stock for an average price of between $50 and $55 a share.