Cities Service Co. continued to search for a new merger partner today as one prospect, Allied Corp., announced it was not interested in what would be about a $5 billion takeover.

Speculation focused on other oil companies, particularly Texaco Inc., but a Texaco spokesman said that company "does not comment on such speculation or rumors."

Although some analysts had expected that Mobil Oil Corp. might make a bid for Cities Service, a Mobil spokesman said the company has "never had any interest in Cities Service and we don't now." Sources said a number of companies in the domestic oil industry are looking at Cities Service, as are a variety of other conglomerates.

The activity followed last week's announcement by Gulf Oil Corp. that it was abandoning its $5.1 billion tender offer for Cities Service in light of continuing antitrust objections to the merger by the Federal Trade Commission.

Cities Service countered yesterday by filing a bitter, $3 billion breach-of-contract suit against Gulf, while FTC officials have said repeatedly that they thought their problems with the takeover could have been solved by a divestiture plan.

It was unclear, however, precisely why Allied Corp., the New Jersey-based oil, gas and chemicals conglomerate, chose not to make a move for Cities Service. One source said that Edward L. Hennessy Jr., Allied's chairman, as a general rule will look at any takeover candidate in businesses related to his firm, which until last year was known as Allied Chemical Corp.

Over the weekend, Hennessy showed interest in Cities Service, but this morning Hennessy and Allied's financial advisers became disenchanted with the deal. At 12:40 p.m. today, the company issued a terse statement saying it had concluded its analysis of Cities Service and has "no interest in acquiring that corporation."

Nevertheless, the prospect that Cities Service is seeking a buyer and is also prepared to buy back as much as $20 million of its own stock to maintain its selling price pushed Cities Service stock up 1 3/4 to 32 1/8. There was no indication when Cities Service might jump into the market.

More than 2.4 million shares of Cities Service stock were traded on the New York Stock Exchange today, almost 2 1/2 times the volume of the second most actively traded security. Gulf Oil stock fell 1/2 to 24 1/2, largely a result of the publicity over the Cities Service suit.