UN Secretary General Ban Ki-moon has said the alleged chemical weapons attack near the Syrian capital "needs to be investigated without delay".
He is sending disarmament chief Angela Kane to Damascus to press for an investigation, his spokesman Eduardo del Buey said on Thursday.
Earlier, France said a "reaction with force" might be needed.
Meanwhile, UN agencies say the number of children forced to flee Syria has reached one million.
The UN's refugee agency and Unicef described the figure as "a shameful milestone", saying a further two million children are displaced within the country.
Activists say hundreds were killed in Wednesday's attack on the Ghouta area of Damascus.
The Syrian government has described the allegations of chemical weapons' use as "illogical and fabricated". The Syrian army said opposition forces had made up the claims to divert attention from their recent huge losses.
"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 Ban Ki-moon, speaking the South Korean capital, Seoul, on Friday.
"Any use of chemical weapons anywhere, by anybody, under any circumstances, would violate international law," he went on. "Such a crime against humanity should result in serious consequences for the perpetrator."
The UN has asked the Syrian government to allow a team of UN weapons inspectors already in the country to investigate the latest incident.
But the government, which denied the allegations, has given no indication that it will allow this.
The investigators, who arrived in the city on Sunday and are staying about 15km (10 miles) from the site of the recent attacks, only have a mandate to visit three other sites of alleged chemical weapons use.
These include the northern town of Khan al-Assal, where some 26 people were killed in an alleged chemical attack in March.
Meanwhile, international clamour over the alleged attacks on Wednesday has continued to grow.
Speaking on French BFM TV, French Foreign Minister Laurent Fabius warned that France must react "with force" if the use of chemical weapons was confirmed.
While he did not elaborate on whether that meant backing military action, he did rule out the idea of deploying troops inside Syria.
The US state department said it was urgently gathering information to try to determine what had taken place in Damascus.
President Barack Obama warned last year that the use of such weapons would cross a "red line".
The UK and 36 other countries have formally referred the latest allegations to Mr Ban, and called for inspectors "to be granted the necessary access to enable their investigation into these latest allegations as a matter of urgency".
Despite blocking a UN Security Council statement condemning the attack at an emergency meeting on Wednesday, Russia is supporting calls for an investigation.
The Kremlin suggested the attack could have been "premeditated provocation" by opposition forces in an attempt to win the backing of the UN.
Opposition activists said that more than 1,000 people were killed after government forces launched rockets with toxic agents into the Damascus suburbs in the Ghouta region early on Wednesday.
The BBC has been unable to independently confirm the death toll.
Activists said Wednesday's attack took place as part of heavy government bombardment in the region surrounding Damascus, with government forces trying to drive out rebel forces. The areas affected included Irbin, Duma and Muadhamiya.
Video footage shows dozens of bodies with no visible signs of injuries, including small children, and survivors being treated in makeshift hospitals, with victims, including many children, having convulsions.
Chemical weapons experts have told the BBC that footage appears genuine and that the injuries shown are consistent with nerve agents.
While it is not clear how many died in the bombardment of the sites and how many deaths were due to any exposure to toxic substances, experts say it would be almost impossible to fake so many dead and injured including children and babies.
Both the rebels and government forces have accused each other of using chemical weapons throughout the 28-month conflict.
Syria is believed to have large undeclared stockpiles of mustard gas and sarin nerve agent.
The government has implied it has chemical weapons, but said they would not be used against civilians.
More than 100,000 people are believed to have been killed during the 28-months of conflict Syria.