By Christiaan Hetzner and John O'Donnell
Late on Tuesday, the ball-bearing maker announced the terms of its proposed takeover after winning control of more than a third of Continental's shares through a web of options organized for it discretely by banks.
If Schaeffler succeeds in buying the Hanover-based group, which is three times its size, it would be the first time a German family business takes over a company listed on the country's blue-chip DAX index.
The takeover, which would also see Schaeffler take on Continental's 11-billion-euro-plus debt pile, would be the biggest so far this year in Europe and put the car-parts supplier nose-to-nose with Germany's Bosch.
Continental is working with Goldman Sachs to mount a defence against Schaeffler, owned by German billionaire Maria-Elisabeth Schaeffler.
Schaeffler chief Juergen Geissinger had sought to calm management fears, saying that he did not intend to break up Continental or slash jobs. Both firms, he said, were a good fit.
But on Wednesday, Continental's Chief Executive Manfred Wennemer told shareholders not to accept the offer and pledged to fight for the company's independence.
Schaeffler's offer of 69.37 euros per share in cash, he said, did not reflect the full value of the company. Continental's stock was trading slightly down at 73.17 euros, after strong gains in recent days.
"There is no convincing strategic rationale for a business combination," Continental said.
Continental was built through a series of acquisitions of high-tech car parts makers, bought with money earned selling car tyres.
Weakened by heavy borrowing to pay for its roughly 11 billion euro purchase of VDO -- which makes the technology inside satellite navigation and fuel injection systems -- Continental now faces a slowdown in car buying as high oil prices bite.
Over the past year, like many rivals, Continental's stock has suffered. Before this week's bounce, it had halved in value.
It had long been speculated that a private equity firm might buy Continental, but those investors rely heavily on debt and the credit crunch makes it harder for them to compete with often cash-rich trade buyers.
Schaeffler's move is similar to that of Porsche's <PSHG_p.DE> takeover of Volkswagen <VOWG.DE>. The smaller sports car maker also bought a stake of 30 percent, made a token takeover bid and is now covertly creeping towards majority control.
(Additional reporting by Arno Schuetze in Hanover)
(Editing by Erica Billingham)