Damascus itself dismissed the accusation as "lies".
The UN secretary general said that arming either side in the 27-month Syrian conflict that has cost tens of thousands of lives "would not be helpful".
Ban told reporters he has been "consistently clear that providing arms to either side would not address this current situation. There is no such military solution."
The harder US line also dismayed Moscow, which had been working with Washington to organise a peace conference.
The Kremlin's top foreign policy adviser Yury Ushakov also said the US decision to provide military aid to Syrian rebels would damage international efforts to end the conflict.
Russian President Vladimir Putin and US President Barack Obama are to meet at the G8 summit in Northern Ireland on Monday.
The US decision to up the ante also prompted expressions of concern from neutral countries such as Sweden, which warned of the risks of an arms race between the rival foreign supporters of the regime and the rebels.
US officials refused to rule out moving towards arming rebels or imposing a no-fly zone, and said Washington would provide backing to the rebel Syrian Military Council.
"The president has made a decision about providing more support to the opposition. That will involve providing direct support to the SMC. That includes military support," deputy national security adviser Ben Rhodes said, declining to elaborate.
Britain and France, which had already said publicly that they believed the Syrian government had resorted to use of its chemical weapons stockpiles, welcomed the US announcement.
"The American decision to arm armed terrorist groups demonstrates... The direct involvement of the United States in the Syrian bloodbath," state news agency SANA quoted a foreign ministry official as saying.
It "raises serious questions about their good faith when it comes to finding a political solution in Syria," the official added.
