CSN received only 8.5 percent of shareholder backing for its offer to buy 33.3 percent plus one share in Cimpor for 6.18 euros per share.
An earlier bid by CSN in December at 5.75 euros a share kicked off a battle between Votorantim Cimentos, Brazil's largest cement producer, and rival Camargo Correa for Cimpor's cement business in Brazil.
They covet Cimpor - Brazil's fourth largest cement maker - ahead of an anticipated building boom as the country gears to host the World Cup and the Olympics in coming years.
Neither Votorantim nor Camargo Correa entered Cimpor to remain a minority shareholder and one of the main goals was to have access to (Cimpor's) cement assets in Brazil, said Banif analyst Rita Carles.
Votorantim built up a stake of more than 20 percent while Camargo Correa now holds just over 30 percent of Cimpor.
Cimpor's market capitalisation is about 4 billion euros ($5.4 billion), according to Thomson One. Its shares fell nearly 5 percent on Tuesday.
Analysts said CSN could still maintain its interest in Cimpor.
Apparently, Votorantim and Camargo managed to keep CSN away. But that is not guaranteed as CSN can build up a stake by buying in the market, said an analyst at a Portuguese bank who asked not to be named.
Even if they could keep CSN away, the two companies will sooner or later have to battle it out, the analyst said.
Trade in Cimpor shares were suspended at the open until after the announcement of the result. When they resumed trading they fell as low as 5.46 euros per share and at 1332 GMT they were 4.85 percent lower at 5.569 euros.
Cimpor also has cement operations in fast-growing emerging markets such as China and Egypt. (Additional reporting by Sergio Goncalves and Filipa Cunha Lima; Editing by David Cowell) ($1 = 0.7361 euro)