The European Union delegation to Khartoum said in a statement that it "noted with concern" reports of the bombing, stressing that hospitals are protected civilian facilities under international law.
Failure to distinguish between the military and civilians "represents an indiscriminate attack and is a war crime," the statement said.
The embassies of the United States and Canada have said they were "appalled" by the reported May 1-2 attack near the Mother of Mercy Catholic Hospital in the Nuba Mountains of South Kordofan state that caused some injuries.
Last week, a former Catholic bishop for the area, Macram Max Gassis, accused Sudan of "deliberate targeting and bombing" of the medical facility which serves more than 150,000 people a year.
It is the only hospital in the Nuba Mountains.
Almost three years of fighting between the government and Sudan People's Liberation Movement-North (SPLM-N) in South Kordofan and Blue Nile states has displaced or severely affected more than one million people, the United Nations says.
Aid agencies have had no access into SPLM-N areas from within Sudan since 2011.
The alleged bombing occurred on the same day African Union-led peace talks between the government and rebels were suspended, tentatively to resume later in May.
"The EU delegation calls on the government of Sudan and the SPLM-N to facilitate full humanitarian access to the conflict-affected civilian populations without delay and to spare no effort in the ongoing negotiations with the aim of speedily reaching a peaceful settlement", the statement said.
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