Hyundai has struck a deal so it can mitigate the losses it has already suffered, it said in a statement emailed to Reuters.
The company reported at the end of December that it was "impossible" to continue construction of the southern bridge because Chile's Ministry of Public Works was trying to expand the scope of the contract without due compensation.
The firm leads the Puente Chacao Consortium (CPC), which won the $740 million tender in 2013 to link the continent with the Chiloe archipelago, some 1,000 kilometers south of Santiago.
The Chilean government claimed HDEC had sought to increase the cost of the project by 50%, or $300 million, a request rejected by the current government of President Sebastian Pinera.
Last Thursday, Pinera said bridge construction was going ahead, adding: "there were some differences that have to do with costs and who should bear them, but that is already resolved."
On Monday, the company said it has given ground on unspecified areas to allow the stalled project to get back on track.
"This agreement requires Hyundai to give up several of its rights in order to reach an agreement and mitigate the losses it has suffered so far, which demonstrates its commitment to Chile and the Chacao project," said Ji Sang Ju, vice president of HDEC's Infrastructure and Environment division.
The agreement is expected to be formalised in later February, the statement added. A spokesman for the CPC did not immediately respond to a Reuters request for further information.
(Reporting by Natalia Ramos in Santiago; Writing by Aislinn Laing; Editing by Matthew Lewis)
By Natalia A. Ramos Miranda