Hamas spokesman Mushir al-Masri's comments on Thursday coincided with an Israeli newspaper report that the EU had given some low-level diplomats permission to meet representatives of the group's political wing.
In Brussels, EU officials said they had reached no collective decision on whether to change their policy towards Hamas.
Al-Masri said the mayors, elected in local council polls over the past several months, had discussed international assistance and the current de facto ceasefire with Israel with EU diplomats in recent meetings.
"Hamas is open to dialogue with all countries except the Zionist enemy, which occupies the land and kills our people," al-Masri said.
More than 3000 Palestinians have been killed by Israel since the start of the second intifada (uprising) in 2000. In the same period, Palestinian resistance movements are accused of killing more than 900 Israelis.
Hamas has recently made a good showing in local elections.
British Foreign Secretary Jack Straw disclosed last week that diplomats from his country had met officials from Hamas' political wing on two occasions.
But he said Britain would not have contact with Hamas leaders until the group renounced violence.
In an unsourced report, the Haaretz daily said the EU decision had surprised the US - a co-sponsor with the EU, Russia and the United Nations of the Middle East peace road map - and raised Israeli concerns.
The US also classifies Hamas as a terrorist group.
"Hamas is open to dialogue with all countries except the Zionist enemy, which occupies the land and kills our people"
Diplomats in Washington have said the US is showing signs of easing its hardline approach towards Hamas in response to the group's growing political influence. But the White House has said there has been no such change.
Tel Aviv, which rejects any contact with Hamas, on Thursday protested against increasing EU contact with Hamas and pressed EU officials to maintain their official designation of the group as a terrorist organisation.
"We believe Europeans should be strengthening moderate
Palestinians and not appeasing the extremists," said Israeli Foreign Ministry spokesman Mark Regev.