Many asylum seekers in Cyprus want to go elsewhere in the EU
The European Commission has called for fairer and more efficient procedures across the EU for asylum seekers.
EU Justice Commissioner Jacques Barrot said the 27-nation bloc should provide "higher standards of protection, a more equal level playing field".
The commission says asylum seekers ought not to be sent back to EU member states that "cannot offer them an adequate standard of protection".
Greece in particular has been accused of neglecting asylum seekers' rights.
In April this year the UN refugee agency, the UNHCR, advised EU governments to refrain from returning asylum seekers to Greece until further notice.
It said a substantial number of asylum seekers in Greece were "facing serious challenges in accessing and enjoying effective protection".
Greece and several other Mediterranean countries - Cyprus, Italy, Malta and Spain - have experienced an influx of economic migrants and asylum seekers in recent years, many of them arriving hungry and exhausted after dangerous voyages in overcrowded boats.
Mr Barrot said the EU ought to "ensure that detention is used only in exceptional cases" for asylum seekers.
He called on member states to establish national procedures to identify asylum seekers with particular needs - such as torture victims - and to provide them with appropriate treatment.
He also said asylum seekers should have easier access to jobs in the EU.
The proposals will now be considered by EU governments and the European Parliament.
The EU aims to have a single asylum procedure, with common guarantees, in place by 2012 at the latest.
Mr Barrot proposed that countries struggling to handle large numbers of asylum seekers should be allowed up to six months before being forced to accept back migrants they have moved on to other member states.
More than 200,000 applications were made for asylum in the EU last year.