The decision follows a meeting of the finance ministers who have long resisted attempts to implement Europe-wide taxes.
However, the European Commission remains committed to the principle of environmental taxation, and is expected to propose minimum duties on fuel among the member states.
A unitary carbon tax had been seen by environment ministers in several EU countries as a mechanism for reaching the Rio targets for the reduction of carbon dioxide emissions.
Several smaller nations, including Denmark and Belgium, saw it as a way of meeting international commitments without damaging competitiveness vis a vis their European partners.
The issue has been raised consistently at meetings of environment ministers in the past two years.
However, some of the larger countries, including Britain and France, have more reservations about the principles of European-wide taxation and are more relaxed about their ability to reach their Rio targets.
British officials said that, during discussions at the Essen summit on Friday, heads of government had decided not to proceed with further proposals for a unitary tax.UK diplomats welcomed the move, arguing that it was a victory for decentralised decision-making.
However, the principle of environmental taxation has not been dumped. Britain might be more sympathetic to proposals for minimum levels of duty - although even this might provoke opposition from Eurosceptics in Britain.