Bulgaria and 14 EU countries want "new ways" to deal with irregular migrants, including sending some of them to third countries.
The request comes as the bloc plans how to implement recently adopted changes to its asylum rules, AFP reports.
The countries presented their joint position in a letter to the European Commission.
Austria, Bulgaria, Cyprus, the Czech Republic, Denmark, Finland, Estonia, Greece, Italy, Latvia, Lithuania, Malta, the Netherlands, Poland and Romania signed the letter.
They want the EU to strengthen its asylum and migration pact, which introduces stricter border controls and seeks to speed up the deportation of rejected asylum seekers.
The pact, which is due to come into force in 2026, will speed up the screening of people arriving without papers and create new border detention centres.
The fifteen countries also want to see mechanisms to detect and intercept migrant boats and take them "to a pre-determined place of safety in a non-EU partner country where durable solutions can be found for these migrants".
They said it should be easier to send asylum seekers to third countries while their claims for protection are assessed.
As a model, they pointed to the controversial agreement that Italy concluded with Albania, according to which thousands of asylum seekers could be taken to detention camps in the Balkan country outside the EU while their cases are being examined.
The European Commission said it would study the letter, although spokeswoman Anita Hipper added that "all our work and our focus is now on the implementation" of the migration and asylum pact.
Under EU law, people who enter the bloc without papers can be sent to a country outside where they could claim asylum. As long as that country is considered safe and the applicant has a real connection to it.
This condition distinguishes it from the scheme set up by the UK, which is not a member of the EU, under which illegal entrants would be denied the right to claim asylum in the UK and would instead be sent to Rwanda.
Rights groups accuse the African country - ruled with an iron fist by President Paul Kagame since the end of the 1994 genocide in which some 800,000 people died - of a crackdown on free speech and political opposition.
The 15 countries said they wanted the EU to conclude agreements with third countries along major migration routes, citing as an example the agreement the EU made with Turkey in 2016 to take in Syrian refugees fleeing the war.
Camille Le Coz, associate director of the Migration Policy Institute, a think tank, said, "From a legal perspective, these models raise a lot of questions and are very costly in terms of mobilising resources and at an operational level."
She noted that the opening date of the reception centres in Albania, established under the agreement with Italy, has been postponed. /BGNES
