Government forces are said to have carried out a deadly gas attack on the outskirts of Damascus.
"I can think of no good reason why any party, either government or opposition forces - would decline this opportunity to get to the truth of the matter," said Mr Ban.
But he was joined in his call by Russia, which has been cautious of any measure which might be used to attack the Syrian government.
The Russian Foreign Ministry said Minister Sergey Lavrov and US Secretary of State John Kerry had discussed the situation on Thursday, concluding they had a "mutual interest" in calling for the investigation.
The ministry said Russia had asked the Syrian government to co-operate, but questions remained about the willingness of the opposition, "which must secure safe access of the mission to the location of the incident."
But Moscow also cast doubt on the nature of the attack, saying that "new evidence that is starting to emerge increasingly shows that this criminal act was clearly a provocation."
Government troops and opposition fighters clashed fiercely in the Ghouta district of Damascus, where the alleged gas attack took place.
Syrian Deputy Prime Minister Qadri Jamil said that he was personally in favour of a fair, transparent international delegation to investigate the most recent incident.
But he said that would require a new agreement between the government and the UN and that the conditions for such a delegation would need to be studied.
Two UN agencies in Geneva have said the number of registered child refugees fleeing Syria's violence had topped the million mark.
Roughly half of the nearly two million refugees from Syria are children and 740,000 are under the age of 11.
"This one millionth child refugee is not just another number," said Unicef chief executive Anthony Lake. "This is a real child ripped from home ... facing horrors we can only begin to comprehend."