CSN, or Companhia Siderurgica Nacional, offered 5.75 euros per Cimpor share, a 5 percent premium to Thursday's close.
By 1440 GMT on Friday, Cimpor shares were up 15.3 percent to 6.30 euros, with analysts saying CSN would have to raise its offer to succeed. CSN shares fell 3.5 percent to 56.54 reais.
Cimpor did not comment on the value of the bid when announcing it had received the approach.
Millennium analyst Joao Mateus said the business rationale for CSN's takeover bid was boosted by the potential for the construction and cement areas in Brazil, especially with the 2016 Olympic Games and the 2014 (soccer) World Cup.
(But) they will surely have to review the price upwards as it is completely outdated, the Lisbon-based analyst said.
A spokesman for CSN in Lisbon said the offer was fair and represents a significant value-added on the average share price in the last six months. CSN opened its first cement business unit in Brazil earlier this year.
Cimpor, which has net debt of 1.8 billion euros, is Portugal's biggest cement maker with growing operations in a large number of countries including Brazil, China, Egypt, South Africa, Spain, and Turkey.
The offer is part of CSN's business diversification and internationalization strategy. The acquisition of control in Cimpor will provide access to consolidated markets and new markets with a high growth potential, Cimpor said.
Cimpor trades at 14.4 times 2010 earnings compared with French cement maker Lafarge at 14.2 and Swiss Holcim at 16.5, according to Thomson One.
Cimpor has a number of large shareholders, including Portuguese construction company Teixeira Duarte with a 23 percent stake and French cement maker Lafarge with 17 percent while state-owned Portuguese bank Caixa Geral de Depositos holds 9.6 percent.
A Portuguese finance ministry spokeswoman said the government would not interfere with the proposed deal and it was up to the shareholders to decide. In the case of CGD it is its board that is exclusively responsible for the matter.
Lafarge said it would not comment and other shareholders were not available for comment.
The fact that the shareholding structure is fragmented is what makes this takeover bid desirable. Recent news on shareholder instability makes the timing very appropriate, Mateus said.
BPI analyst Bruno Silva said the bid could open the door for a fight for control at Cimpor, adding there was potential for an upward revision of the offer price.
In Sao Paulo, CSN said it planned to fund the takeover through a mix of cash in hand and bank loans.
The bid signaled increasing muscle by emerging economic powerhouse Brazil to expand abroad, following a trend during the economic crisis of Chinese and Indian companies snapping up companies in other markets.
Banco Espirito Santo is advising CSN.
(Additional reporting by Patricia Rua, Shrikesh Laxmidas, Sergio Goncalves, Andrei Khalip and Cesar Bianconi; Editing by Dan Lalor)
($1 = 0.6949 euro)