The bloc, which this week imposed sanctions against Yahya Sinwar, the political leader of Hamas in Gaza, has been working for several weeks to create a specific sanctions regime against the group after its deadly attack on southern Israel on Oct. 7.
"These measures target individuals and ban money transfers," Christophe Lemoine told reporters at a weekly press briefing.
The United States and Britain have already imposed sanctions targeting officials who advance Hamas' agenda and interests abroad and help manage its finances.
Hamas, which is designated as a terrorist organisation by the European Union and the United States, has established a secret network of companies managing $500 million of investments in companies from Turkey to Saudi Arabia, the U.S. Treasury has said.
Israel, whose forces have been pounding Gaza for weeks to try to eliminate Hamas in retaliation for the Oct. 7 attack, has long accused Iran's clerical rulers of stoking violence by supplying arms to Hamas.
While much international attention has focused on the cross-border assault and Israel's subsequent war, European officials have also expressed increasing concern about rising violence against Palestinians in the West Bank.
U.N. figures show daily settler attacks have more than doubled since the Hamas attack and Israel's assault on Gaza.
Lemoine said the foreign ministers would continue talks on Monday over measures aimed at violent settlers. France is already working on its own national framework.
Some diplomats have predicted it will be hard to get unanimity for EU-wide bans, as countries such as Austria, the Czech Republic and Hungary are staunch allies of Israel.
France, along with the Netherlands and Belgium, have proposed designating 12 people to be sanctioned for human rights abuses in relation to settler violence, but there is still no consensus among member states, one European diplomat said.
(Additional reporting by Andrew Gray in Brussels and Sabine Siebold in Berlin;Editing by Tassilo Hummel, Sudip Kar-Gupta and Ros Russell)
By John Irish
