Ministers said after a meeting in Luxembourg that some of the 500 million euro ($600 million) cut in funding to the Palestinian government would now be channelled via humanitarian aid organisations.
Jack Straw, the British foreign secretary, said: "We do not wish to punish the Palestinian people for the decision they freely made to elect a Hamas-dominated government.
"At the same time, Hamas has got to recognise that being elected as a government, democratically, they have responsibilities as democrats to do what everybody else has to do as democrats, which is to eschew violence."
Javier Solana, the EU foreign policy chief, said that the Palestinians were not being abandoned and that the EU "will do business as usual with the Palestinian people".
However, Ben Bot, the Dutch foreign minister, said: "The Palestinian people have opted for this government, so they will have to bear the consequences."
The EU had threatened to suspend the aid unless the Hamas government agreed to renounce violence, recognise the state of Israel and abide by previous Palestinian agreements.
Palestinians in the Gaza Strip reacted defiantly to the news and hundreds of youths took to the streets to protest against the decision.
"Why are you starving us?" protesters shouted while hurling eggs at the UN headquarters in Gaza, where an EU team is also based.
"The breakdown in the provision of public services would imply effects that go beyond a humanitarian crisis."
Pierre Kraehenbuehl, ICRC
Aid agencies have also voiced concerns about the potential impact of a cut in aid.
The Palestinian Authority employs 140,000 people in the Gaza strip and Omar Abdel Razak, the authority's finance minister, said that most would go unpaid for the time being.
"The Gazan population is extremely dependent on donor aid so, when it is reduced, it has an immediate consequence on the ground," said John Ging, head of the UN agency for Palestinian refugees (UNRWA) in Gaza.
"We are concerned about the consequences on the security side. If the security forces are not paid, how will they express that frustation, what will that mean for the general security in Gaza?"
The International Committee of the Red Cross said that Palestinians already face "extreme hardship" because of a deepening economic crisis stoked by Israeli restrictions on the movement of people and goods, imposed on security grounds.
Cutting off funding to the Palestinian Authority could provoke a "broader humanitarian emergency" if the administration is unable to provide services such as water supplies and medical care, said Pierre Kraehenbuehl, director of operations for the organisation.
"The breakdown in the provision of public services would imply effects that go beyond a humanitarian crisis," he said.