The deal raises the odds of Actividades de Construccion y Servicios gaining a strategic holding in Hochtief and becoming the largest public works group in Europe and number three worldwide.
Two million shares represent roughly half of Southeastern's 4.84 percent stake in Hochtief and the move came after ACS made an improved offer of nine of its own shares for five of those in Hochtief.
Southeastern, which is based in the United States and owns around 6.5 percent of the Spanish company, said in a statement that its decision was also a reaction to how Hochtief directors have handled the boardroom saga so far.
A Southeastern statement cited "a management team in which we have lost confidence" owing to "recent unacceptable steps," a reference to Hochtief's defensive sale of a 9.1 percent stake to Qatar. That was a measure aimed at ACS but it diluted the holdings of all shareholders, including Southeastern.
Southeastern also said that the new ACS offer, up 12.5 percent on the initial bid, is "more reflective of the intrinsic value of Hochtief."
ACS currently owns around 27.2 percent of Hochtief and with the stake it stands to acquire from Southeastern, it will own close to 30 percent of the German firm. That is the level at which ACS must make a full takeover bid for Hochtief under German law.
ACS's offer has not met with great success so far and was formally opposed by Hochtief management on Wednesday, although chairman Herbert Lütkestratkötter suggested talks with ACS "could begin shortly."
The German company also told investors in a statement that there was no reason for hasty decisions.
Equinet analyst Ingbert Faust said: "At current prices, there is no reason for Hochtief shareholders to accept the offer" by ACS.
Hochtief is active in Germany and in other dynamic regions worldwide, while ACS is strong in Spain, a country currently facing economic uncertainty.
If a full offer for Hochtief is not successful, once ACS has passed the level of 30 percent it could buy smaller amounts of the German group on the stock market and take it over bit by bit.
The ACS bid for Hochtief was launched on December 1 and remains valid until December 29.