Spanish construction giant Ferrovial offered 687 million euros ($875 million) to buy Australian firm Transfield Services, which rejected the bid as poor value, the companies said on Monday.
But Transfield held open the door for further possible negotiations.
It was the latest move in Ferrovial's overseas expansion after it struck a deal last week to buy three British airports, a promising sign for Spain's battered construction sector.
Ferrovial submitted "an indicative, non-binding proposal" to buy 100 percent of Transfield Services at 1.95 Australian dollars per share, it said in a statement.
It called that a "compelling proposition" for shareholders which offered a "substantial premium" on Transfield's recent average share price.
Transfield said in a statement that the offer, worth the equivalent of 687 million euros, undervalued its shares, however.
"The board believes that shareholders' interests are best served by conducting exploratory discussions with Ferrovial to determine whether a proposal which would deliver better value to shareholders can be put forward," it said.
Ferrovial said it "reserves the right to withdraw the proposal at any time".
"Australia is a key target market for Ferrovial, along with Spain, Poland, UK, USA, Canada and Chile," said analysts at Citi Research in a note on Monday.
"We believe Ferrovial will likely raise its offer price in order to secure approval from Transfield's board."
Transfield Services runs maintenance and construction operations across various industries in 10 countries.
Ferrovial, specialising in infrastructure and construction, holds a 25-percent stake in London's Heathrow, one of the world's busiest airports.
Ferrovial was hit by the crash of Spain's domestic construction sector in 2008 and last year was forced to sell part of its stake in Heathrow, but it has recently relaunched its overseas expansion.
Last week Ferrovial teamed up with another Australian firm, Macquarie, to buy airports in the British cities of Aberdeen, Glasgow and Southampton for 1.3 billion euros.
That deal is subject to approval by European regulators and is expected to be sealed by January 2015.
Ferrovial is also one of three companies that have had bids accepted to take a stake in Spain's state airport operator Aena. The government hopes to make billions of euros out of that major privatisation.
After the news of the failed bid, Ferrovial's shares fell by 1.08 percent on the Madrid stock exchange early Monday afternoon to trade at 15.08 euros. The IBEX-35 leading stock index was down by 1.10 percent overall.