The Paradise Papers leak last month gave a new impetus to the plan, making public some of the intricate ways the world's rich evade tax using offshore havens.
The EU has struggled for over a year to finalise the blacklist, with smaller, low-tax EU nations such as Ireland, Malta and Luxembourg worried about scaring off multinationals.
Britain fought particularly hard against the list, afraid that its crown dependencies, including Jersey and the Virgin Islands, would be singled out.
Other jurisdictions are understood to have been given leeway after suffering severe damage during hurricanes in the Caribbean earlier this year.
European Economic Affairs Commissioner Pierre Moscovici said officials from member states were negotiating from an initial list of 29 countries, with divisions still strong over the weekend on who will make the final version.
"Since Thursday, we have entered a phase of intense political and diplomatic activity," Moscovici told reporters on Monday.
"And I do see a risk that some countries whose names were quoted in the many tax scandals over the last five years may not be listed. That would be strange," he warned.
Enforcement problem
Enforcement is the biggest problem, with EU countries split over whether blacklisted countries should be subjected to financial sanctions or if the list is shaming enough itself.
Several states, including France, support tough measures against the listed tax havens such as exclusion from EU and World Bank funding, though the debate is still open.
Other countries are reluctant to draw up common sanctions, believing that responsibility is better left to member states.
An existing list of tax havens compiled by the Organisation for Economic Cooperation and Development (OECD) currently includes only Trinidad and Tobago.
By contrast, the EU originally screened a total of 92 jurisdictions and once the list is compiled it is expected to be continuously updated.
In a blow to activists, states that charge no corporate tax are not automatically considered at risk of breaching EU tax criteria.
However, the criteria do single out countries that facilitate the creation of shell companies and other structures that could aid tax avoidance.
Countries in the EU's firing line have been given an opportunity to stay off the list if they provide a political commitment and a detailed plan to comply.
All countries, which initially included the US, were given until Tuesday's meeting of the EU's 28 finance ministers to provide feedback and possible measures to satisfy EU demands.
Officials said the EU ministers would likely create a so-called grey list comprising of countries with severe tax evasion issues, but who have made commitments to change their ways.
The list is the latest international effort to clamp down on tax avoidance -- increasingly seen as a moral issue -- following the OECD's move to compile a list of "uncooperative tax havens".
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