The move followed an agreement with Sudan and African countries in the UN Human Rights Commission, a representative of Luxembourg, the current head of the EU. told the body.
"The European Union and the co-sponsors wish to withdraw the draft from the agenda," the diplomat said, shortly before the draft was due to be debated in the 53-member Commission
She said cooperation with the African group and Sudan had "produced an agreement which offers the best chance of halting human rights violations in Sudan, which we are concerned about and which we condemn".
The EU was expected to rally around an alternative and milder African motion expressing "deep concern" at continued human rights violations by both sides in Darfur.
The provisional African draft, which has yet to be debated in the Commission, also calls on Khartoum and rebels in Darfur to resume peace talks, respect a ceasefire agreement, and extends the mandate of a UN human rights expert probing Sudan.
Full details of the agreement were not revealed.
About 300,000 people are estimated to have died and more than two million forced out of their homes during more than two years of conflict between Khartoum and rebels in Darfur.
The partly political and partly ethnic conflict in Darfur pits rebel groups from the local population of black African origin against government troops and Khartoum-backed Arab militia, the Janjaweed.
The motion withdrawn Thursday had sought condemnation of "the fact that most attacks have been deliberately and indiscriminately directed against civilians, many of them under the direct responsibility or tolerated by the government of Sudan".
It had also expressed "grave concern at continuing, widespread and systematic violations of human rights and breaches of international humanitarian law in Darfur that may amount to war crimes and crimes against humanity".
Khartoum had warned the United Nations this week against appointing a special human rights rapporteur for Sudan, arguing such an "irrational" move would only complicate the Darfur crisis.