One of the aims of the rules, known as the Markets in Financial Instruments Directive, or MiFID II, is to make it easier for people to choose where to clear the listed derivatives contracts they buy and sell.
This would be done through the "open access" rule, which stops any requirement to clear a derivative contract within the same exchange group that traded the contract.
But Britain's Financial Conduct Authority (FCA) said it received applications for an open-access waiver from ICE Futures Europe (>> Intercontinental Exchange Inc) and from the London Metal Exchange (>> Hong Kong Exchanges and Clearing Limited).
This means the exchanges would not yet have to make changes to allow customers to clear contracts elsewhere.
The FCA said it has decided to grant transitional arrangements in the interests of ensuring there is an "orderly functioning market".
"Accordingly, with effect from 3 January 2018, ICE Futures Europe and LME will not be required to consider open-access requests ... as they relate to exchange-traded derivatives, until the expiry of the transitional period on 3 July 2020."
BaFin, the German markets regulator, announced late on Tuesday that it had granted the same time-limited waiver to Deutsche Boerse's (>> Deutsche Boerse) Eurex Clearing arm.
Open access has been a feature of share trading and clearing for many years, but its introduction to listed derivatives has proved divisive.
Some EU policymakers and Deutsche Boerse had warned about financial stability risks from opening up derivatives clearing to competition, but critics had said this was an excuse to prevent competition.
(Reporting by Huw Jones; Editing by David Goodman)