The A$715m ($524m; Â£347m) offer, made in December, was described as too low and opportunistic.
Ferrovial first attempted to buy the company in late 2014 but abandoned the bid after failing to get support from Broadspectrum's board.
Shares in Broadspectrum closed 1.2% lower on Thursday.
Broadspectrum, which last September changed its name from Transfield Services, is an outsourcing and construction services company.
It operates in several sectors, including infrastructure, property, defence and financial services.
One of its biggest revenue sources comes from a contract to run Australia's offshore detention centres on Papua New Guinea's Manus Island and on Nauru in the Pacific.
Human rights groups have criticised the management of the centres and the company has faced allegations of abuse and sexual misconduct by its employees.
Australia offshore detention centre operator Broadspectrum has rejected a second hostile takeover bid from Spanish infrastructure firm Ferrovial.