The Mexican group, the world’s third largest cement maker, has also extended the offer period by 3 weeks to July 16.
The offer of US$15.85/share, which was revised on April 10 from an initial offer of US$13.00, was due to close today.
Cemex took control of the Rinker board on Tuesday after moving over the 50 per cent acceptance level on June 8.
Rinker earns about 80 per cent of its revenue in the US.