Ban asked Qatar and some other Arab nations to stop arming the militants, UN spokesman Martin Nesirky said on Monday, press tv reported.
"The secretary general called for stemming the supply of arms to any side in the Syrian conflict. More arms would only mean more deaths and destruction," Nesirky said.
Ban made the appeal in a meeting with Arab League Secretary General Nabil Elaraby and Qatar's Prime Minister Hamad bin Jassim bin Jaber Al Thani at the UN headquarters in New York City.
The UN chief also "reiterated his call on the (UN) Security Council to find unity and put all of its weight behind a political solution in Syria," said the UN spokesman.
Qatar has been leading efforts to supply the militants in Syria with more heavy weapons.
The Syria crisis began in March 2011, and many people, including large numbers of soldiers and security personnel, have been killed in the violence.
The Syrian government says that the chaos is being orchestrated from outside the country, and there are reports that a very large number of the militants are foreign nationals.
In an interview recently broadcast on Turkish television, Assad said that if the militants take power in Syria they could destabilize the entire Middle Eastern region for decades.
"If the unrest in Syria leads to the partitioning of the country, or if the terrorist forces take control... the situation will inevitably spill over into neighboring countries and create a domino effect throughout the Middle East and beyond," he added.
