Today's statement was issued by the EU's commissioner for development and humanitarian aid, Poul Nielson.
He said the EU has been funding the work of CARE -- the aid organization Hassan headed in Iraq -- for more than a decade. Hassan's murder, the statement says, has deprived the EU's aid office of a "valued colleague and a true humanitarian."
Nielson's statement was read out to journalists today by commission spokesman Jonathan Todd: "I was horrified to learn about the reported brutal murder of the aid worker, Margaret Hassan. My thoughts are with her family, and with the needy people of Iraq who have lost such a good friend. In peace and war, Margaret dedicated her life to helping vulnerable Iraqis, most recently through the humanitarian organization CARE International."
The statement goes on to warn that the continuing practice of targeting aid workers in Iraq is making further assistance "almost impossible."
"This kind of savagery makes it almost impossible for relief agencies to continue their crucial work in Iraq. The main victims are the innocent and suffering Iraqis that benefited from international aid programs," the statement says.
Another EU spokesman, Jean-Charles Ellermann-Kingombe, said many aid organizations have pulled their Western staff out of Iraq long ago and continued work inside Iraq only with local employees. He said the EU has nevertheless been able to carry out most of its humanitarian projects, totalling almost 100 million euros ($130 million) since the war.
But, Ellermann-Kingombe added, now some aid agencies have begun completely pulling out of Iraq. He said work inside Iraq is becoming increasingly difficult, "though still not entirely impossible."
The EU's humanitarian aid arm, known as ECHO, is still able to finance 20 ongoing projects in Iraq.
Commission spokeswoman Emma Udwin said that money put aside by the EU to support elections in Iraq can also be put into use. She confirmed an earlier pledge of 30 million euros will go ahead. She said the money becomes "useful as soon as it is delivered."
However, speaking privately, one official said all EU personnel in the region currently operate out of Amman. This will also be the case for EU-run courses for Iraqi electoral workers and other training work.
Three EU officials will travel to Baghdad in advance of the January elections to act as advisers to the Iraqi authorities. However, a significant part of their 1.5 million-euro budget will go toward ensuring their security.
EU officials have earlier told RFE/RL that a possible "rule of law mission" to Iraq after the elections to support judicial and law enforcement reforms could be difficult to staff, as EU member states appear increasingly reluctant to risk the lives of their citizens.