The allegations of chemical-weapons use in suburbs east of the Syrian capital must "be investigated without delay," Ban said at a diplomatic event in Seoul.
His call came a day after the world body officially demanded the Assad regime let U.N. inspectors already in Syria looking into earlier claims of chemical-weapons use be granted immediate access to the stricken areas where more than 1,100 people were reported by the opposition to have been killed in regime nerve-gas attacks Wednesday.
"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," Ban said at the Seoul event.
"Any use of chemical weapons anywhere, by anybody, under any circumstances, would violate international law. Such a crime against humanity should result in serious consequences for the perpetrator."
The Assad regime has denied using chemical weapons and given no indication it will allow a U.N. inspection.
Ban sent U.N. disarmament chief Angela Kane to Damascus to press for an urgent investigation, a Ban spokesman said.
Assad-regime forces pressed ahead Thursday with a large-scale shelling offensive in and around the areas allegedly targeted with nerve gas.
Military restrictions would make it difficult if not impossible for the U.N. team to approach the suburban area fewer than 10 miles from the team's Damascus hotel.
Humanitarian agencies reported troubles reaching the heavily damaged suburbs Thursday because of military restrictions, The Wall Street Journal said.
The incursions could also cover up evidence of a chemical-weapons attack, in the event the U.N. team is allowed to visit the site, the Journal said.
The Syrian army vowed on state TV Thursday to "cleanse" suburban Jobar, which opposition groups say was among the areas hit by the alleged chemical-weapons attack.
Jobar also contains the most venerated site for Syrian Jews, an ancient 2,000-year-old synagogue and shrine in commemoration of the biblical prophet Elijah, which has been a place of Jewish pilgrimage for many centuries.
Opposition officials said the Wednesday attack began shortly after 2 a.m., when Russian-type Grad rockets, similar to those the Palestinian Sunni Islamic group Hamas has fired into Israel, were launched -- two from a highway bridge and others from a Damascus factory.
Notable deaths of 2014 [PHOTOS]