The penalty could follow an investigation by German cartel authorities into alleged price manipulation by six RMC subsidiaries.
Peter Young, the chief executive, said an internal investigation - already underway for at least 37 days - had yet to be completed.
The German action, which RMC first highlighted last month, threatened to cast a pall over the group's solid first-half profits. RMC shares fell sharply yesterday, slipping 5.67 per cent to 939p.
"If the Cartel Office's allegations are proved to be correct, the group's subsidiaries are likely to be fined. It is too soon to make an estimate of the size of such fines, but there is a possibility that they may, in total, be material ..." an RMC statement said.
Bob Lambourne, the finance director, said the penalties could amount to 10 per cent of group profits. Last year, RMC made pounds 256m. No provision has yet been made for the possible penalty, which was recorded as a contingent liability.
In total, German officials are investigating more than 50 firms. Eike Sacksofsky, spokesman for the German Federal Cartel Office, said: "We will try to finish these proceedings quickly."
In the six months to 30 June, RMC recorded a 16.8 per cent rise in pre- tax profits to pounds 131m. Turnover rose 7.1 per cent to pounds 2.26bn.
Mr Young said rapid growth in the US and continental European markets outside Germany underpinned the gains. Activity in the UK was stable.
In the US, where RMC operates in 13 states, trading profits rose 118 per cent to pounds 37.9m. In Europe, excluding the UK and Germany, they jumped 34 per cent to pounds 42m.
In Germany, which accounts for 15 per cent of RMC's total profits, difficult trading in the East depressed results.
Stuart Walker, deputy chief executive, said: "There is overcapacity in Germany ... the price pressure is mainly in the east of the country."
Trading profits from German operations sank 31 per cent to pounds 22.4m despite an 8 per cent rise in turnover to pounds 601.5m.
Mr Young foresaw a difficult second half in Germany but remained confident about underlying performance across the group.
RMC spent pounds 114m buying 22 firms in the first half. Since July, a further pounds 65m has been devoted to acquisitions.Reuse content