In what could be the prelude to Europe's biggest takeover battle yet, Mannesmann AG, Europe's second-largest mobile-phone company, tonight firmly rejected a purchase offer from Vodafone AirTouch PLC, the largest mobile operator in the world.

The refusal, delivered during a meeting in Germany today between Vodafone chief executive Chris Gent and his counterpart at Mannesmann, Klaus Esser, was considered likely to touch off a hostile bid from Vodafone. The buyout offer, made as a swap of stock, was valued at more than $105 billion.

Mannesmann, considered one of the hottest telecommunications companies in Europe, called the Vodafone offer "wholly inadequate" and said a combination with Vodafone was not "strategically attractive." The rejection was significant because Vodafone, known for its ambition, was considered likely to respond to the rejection with a takeover offer that could be matched by any number of competitors in magnitudes that could make the whole battle one of the biggest, or even the biggest, industrial takeover in business history.

Vodafone's desire to buy Mannesmann has been no secret for the last few weeks. But in recent days it has become apparent that others also would like to acquire the German telecommunications and engineering company.

Reports in the British press over the weekend said British Telecommunications PLC and Bell Atlantic Corp. also were interested in buying Mannesmann. Officials at British Telecommunications and Bell Atlantic declined to comment.

The race for consolidation in Europe's fast-moving wireless telecommunications industry, which leads the United States in providing access to data and the Internet on mobile devices, has accelerated just in the last few months. And it includes some transatlantic combinations. Last June Vodafone completed its $58 billion acquisition of AirTouch, the largest mobile operator in the United States. In September, Bell Atlantic agreed to combine its wireless business with Vodafone in the United States, making the combined entity the largest U.S. cell-phone provider.

Then last month Mannesmann announced a deal to acquire Orange, Britain's third-largest mobile operator, for about $33 billion. Mannesmann also has controlling interests in an Italian mobile company and a land-line operator. Its occasional partner in ventures on the European continent: Vodafone.

Meanwhile, France Telecom is moving into Germany with the acquisition of that country's third-largest wireless firm, challenging both Mannesmann and France Telecom's former ally, Deutsche Telekom.

Should Vodafone try to acquire Mannesmann, France Telecom is widely seen as a potential buyer for Orange. Deutsche Telekom, meanwhile, has bought a controlling interest in the British cell operator One-2-One.

As the European telecommunications industry is restructuring and consolidating, European business executives also are losing their traditional distaste for hostile takeovers.

In the last year, three big ones have been launched. The French-Belgian oil company TotalFina bid for French oil giant Elf-Acquitaine, Banque Nationale de Paris bid for investment bank Paribas and retail bank Societe Generale, and Olivetti Spa bid for the much larger Telecom Italia.

The oil companies eventually agreed to merge, BNP obtained Paribas but not Societe Generale, and Olivetti won Telecom Italia, for $58-billion, but is having considerable transition difficulties.

Vodafone AirTouch already has access to more than 60 million customers directly or indirectly, according to the company's annual report. In it, Gent writes: "Vodafone AirTouch has the clear aim of becoming, over the next decade, one of the world's largest companies."