"Holcim and Lafarge believe that... there is rationale in considering a potential merger that could deliver significant benefits to customers, employees and shareholders," the two companies said in separate but near-identical statements.
The Swiss company said that talks were at an "advanced" stage.
"The discussions are based on principles consistent with a merger of equals which build on the strengths and identities of the two companies," it said.
It underlined that no agreement had yet been reached, nor was it possible to say if the talks would lead to a definitive merger deal.
On its website, Lafarge describes itself as the global number one for cement, number two for aggregates and number four for concrete.
Industry observers note that the berths in the rankings vary according to methodology.
According to a 2013 ranking by specialised trade magazine Global Cement, which assesses overall output capacity based on a broad range of factors, China's Anhui Conch had an annual output capacity of 217 million tonnes, followed by Lafarge with 205 million tonnes and Holcim with 174 million tonnes.
The combined clout of Lafarge and Holcim would therefore create an industry behemoth.
Founded in Switzerland in 1912, Holcim employs 71,000 people, with production sites in around 70 countries and a market presence on every continent.
In notched up net sales of 19.7 billion Swiss francs (€16.1 billion, $22.2 billion) in 2013.
Lafarge began as a French limestone-quarrying company in 1833, and now employs 65,000 people in 64 countries, with sales of €15.8 billion ($21.7 billion).
After having surged Friday as rumours swirled concerning the merger talks, both companies' shares remained buoyant at the close of trading in Zurich and Paris.
Shares in Holcim soared 6.9 percent to 80.20 francs, while Switzerland's SMI index fell 0.21 percent.
Lafarge's shares jumped 8.9 percent to 64.09 euros, as Paris' main CAC 40 index gained 0.79 percent.