Speaking at a meeting of EU foreign ministers, Benita Ferrero-Waldner, the External Relations Commissioner, said the bloc had done more than any other foreign partner to support the caretaker Palestinian government.
The 25-nation EU has released 120 million euros for Palestinians since January elections in which the militant Islamic group swept to power, threatening to derail the Middle East peace process.
But the EU official noted that the bloc had set out conditions against which it would review funding once a new government was fully in place.
"The new government's positions on violence, on recognition of Israel and on existing agreements like the (Middle East peace) 'road map' remain absolutely crucial," Ferrero-Waldner told reporters in Salzburg, Austria.
"We want to remain a reliable partner for the Palestinian people, but we will not go soft on our principles ... Money will not flow to the new authority unless it seeks peace by peaceful means."
Javier Solana, the EU foreign policy chief, defended the EU's decision to keep funding the caretaker Palestinian government.
"[Hamas'] positions on violence, on recognition of Israel and on existing agreements like the (Middle East peace) 'road map' remain absolutely crucial"
EU External Relations Commissioner
"The (Palestinian) Authority has a gigantic deficit, which could expand even further," he said. "What we have said is that we don't want to abandon the Palestinian people."
He underlined that Hamas remained on an EU blacklist of terrorist organisations. "So we can't cooperate with them legally," he said, but at the same time: "We have to find ways of supporting the Palestinian people."
Asked if Hamas could be removed from the EU blacklist if it met the conditions which would allow aid to continue, the EU official added: "If they do so, yes."
Under the Palestinian constitution, Hamas has three weeks to form a government, but the charter also provides for another 14-day extension.
EU funds have helped keep the
Palestinian government afloat
Ferrero-Waldner voiced hope that Hamas could yet change and meet the EU conditions. "We cannot exclude that Hamas is seriously thinking about how to respond to the situation in the future," she said.
The EU official insisted that it was "premature" to speculate on exactly what funding might be cut if Hamas does take power as expected but does not renounce violence.
But an EU source said it was only natural that EU governments were starting to talk about it.
And to help them the EU external affairs commissioner presented the ministers in Salzburg with a paper detailing the breakdown of different kinds of aid and where exactly the money goes.
It is understood that funds paid directly to the Palestinian government - as opposed to via non-governmental organisations (NGOs) or other linked bodies - would be most likely for the chop if Hamas stands firm.