CRH, the world's third-largest building materials supplier by market value, has decided not to bid for rival PPC, the South African company said today.
This leaves the field clear for rival suitors for the South African company.
Last month PPC said CRH had made an approach with a cash proposal and had been given time to conduct due diligence and then come back with another offer.
"CRH has decided not to submit an updated expression of interest and therefore considers it appropriate to withdraw from the Independent Board's process," PPC said in a statement.
PPC last month turned its back on a takeover attempt by AfriSam, backed by Canada's Fairfax Africa.
However, regulations allow Fairfax until December 12 to post its partial offer circular.
CRH had said in August it had around €5 billion in cash to spend on M&A over the next 18-24 months.
It has committed €3 billion of that to buying Ash Grove Cement and a further $750m on other cement acquisitions in Florida.
A purchase of PPC would have run counter to CRH's recently declared acquisition strategy, with chief executive Albert Manifold saying last month that the firm would concentrate on deals in North America and would not overinvest in developing economies.
A spokesman for Dublin-based CRH said the company had no comment to make.
PPC, which has been a target for industry consolidation for several years, said it was still talking to Switzerland's LafargeHolcim.
LafargeHolcim has said that it is in talks with the board of PPC regarding a possible transaction in Africa, while Dangote Cement, majority owned by Africa's richest man, Aliko Dangote, has also shown an interest.
Dangote Cement made an approach in September, but later withdrew, saying it did not want to get into a lengthy process with an uncertain outcome.
PPC last month reported a 36% rise in half-year earnings, helped by a robust performance in Zimbabwe and Rwanda.
Commenting on the development, Davy analyst Robert Gardiner said that CRH's strategic priority remains its end-markets in Europe and North America so a deal for PPC was always a low probability.
"The group is focused on developed end-markets and preparing to integrate the soon to be completed acquisitions of Ash Grove and Suwannee," the analyst added.
CRH shares closed 0.56% higher in Dublin trade today.