"Yesterday's sickening, savage and apparently deliberate attack on UN-Syrian Red Crescent aid convoy is the latest example."
The United Nations had been forced to suspend aid convoys as a result of the latest outrage.
"The humanitarians delivering life-saving aid were heroes.
"Those who bombed them were cowards.
"Accountability for crimes such as these is essential," he said.
The plight of refugees has been a strong theme at the UN this week with two summits on the crisis, which is the worst it has been since World War II. More than 60 million people are displaced.
Ban also appeared to make reference to the US presidential elections calling on politicians "and candidates" not to engage in the cynical and dangerous political maths that says you add votes by dividingpeople and multiplying fear.
Candidates Hillary Clinton and Donald Trump have been in New York, meeting with various leaders.
CNN reported that Clinton last night met the leaders of Egypt, Ukraine and Japan and that Trump also met the Ukrainian leader.
US president Barack Obama spoke this morning and today is hosting a leaders' summit on refugees.
John Key is due to give his speech about lunchtime today.