Brussels is pushing to provide 5.7 billion euros ($6.8 billion) of fresh support to help Turkey and other countries around Syria host refugees from their neighbour's civil war, according to a proposal seen Wednesday.

Under the European Commission plan, 3.5 billion euros would be provided to Turkey from 2021 to 2024 and the remaining 2.2 billion would go mainly to Lebanon and Jordan.

The proposal — expected to be presented to EU leaders at a summit on Thursday — comes as part of the bloc's push to improve ties with Turkey after a spike in tensions last year in the Eastern Mediterranean.

The additional funding is seen as a key incentive to Turkish President Recep Tayyip Erdogan to stick to efforts aimed at tackling long-running disputes with Greece and cease controversial gas exploration in the waters around Cyprus.

Turkey currently hosts some 3.7 million refugees from the conflict in Syria and has been used by the EU as a bulwark to help stem the flow of migrants into Europe.

Brussels and Ankara struck a deal in 2016 that has seen the bloc give four billion euros so far to Turkey to help it host the refugees in return for preventing crossings and accepting back arrivals from Greece.

A further two billion euros is still set to be disbursed in the coming years under that agreement.

Erdogan has long demanded more assistance to deal with the refugees and has previously threatened to open Turkey's border if the EU does not stump up additional funds.

The new EU proposal says its future assistance "will gradually move from humanitarian priorities to socio-economic support and development" for refugees who need to build lives in Syria's neighbouring countries after over a decade of war at home.

The plan for the new funding is part of a range of enticements that the bloc is using to try to keep Erdogan on side, with Brussels also offering to modernise a customs union with Turkey and start high-level talks on issues from health to security.