ACS, which already has a 30-percent stake in Hochtief AG, said it was opening the offer to all shareholders in the company, which is Germany's largest public works group. It offered eight ACS shares for five of Hochtief's.
"The ACS Group has decided to make a tender offer to all shareholders of the German company Hochtief, it said in a statement to Spain's stock market regulator.
The remaining 70 percent stake would be worth about €2.76 billion ($3.61 billion) based on the value of Hochtief's shares at the close of the share market on Wednesday.
The Spanish daily ABC had reported earlier Thursday that ACS would make a takeover offer for Hochtief, prompting a flurry on the stock market.
In Madrid, trading of ACS shares was suspended in the morning but re-opened shortly after midday (1000 GMT), gaining 1.59 percent to €35.35 when compared with Wednesday's close.
Hochtief shares leapt by almost 10.5 percent at the opening of trading on the Frankfurt stock exchange before falling back to show a gain of 3.0 percent
at €58.05 by midday.
A spokesman for Hochtief said the company had "not yet received the offer" from ACS. "If we receive one, we will look into it closely and we will comment on it," he told news agency AFP.
ACS first bought a 25 percent stake in Hochtief in March 2007, and then exercised an option to increase its stake in March of last year. It now owns 29.98 percent of the equity in Hochtief, Germany's largest public works group, according to Hochtief's website.
Dow Jones Newswires quoted Bankhaus Lampe analyst Marc Gabriel as saying a takeover would make strategic sense. The two groups overlap little, and buying Hochtief would propel ACS into global player position, Gabriel said.
Spain's biggest construction group has sought recently to reduce its debt, in particular with the sale in August of a holding in the motorway management company Abertis for €1.72 billion ($2.24 billion).
At the same time, ACS has increased its interests in the energy sector, and is the leading shareholder in the wind energy company Iberdrola, with a stake of 12.6 percent.
The group in July announced first-half net profits slumped 67 percent to €501 million from the same period last year, when earnings were boosted by the sale of its 35-percent stake in energy group Union Fenosa.
The bursting in 2008 of Spain's property bubble, which had been the country's engine of growth for a decade, has hurt construction and real estate firms, and plunged the Spanish economy into its worst recession in decades.
ACS president Florentino Perez is also president of one of the leading European football clubs, Real Madrid.