foreign minister Walid Muallem said a political solution was still possible if the West and Gulf states halted support for the rebels.
Muallem also dismissed the concerns Washington has about the security of Syria's chemical weapons, branding them as a ploy to prepare the ground for an invasion, as he said had happened in Iraq.
The Syrian Observatory for Human Rights said an air strike on the town of Salqeen in the mainly rebel-held province of Idlib bordering Turkey had killed 21 people, including eight children.
At least 18 soldiers were killed in Homs province of central Syria in a rebel ambush and bombing of their convoy on the Damascus-Palmyra highway, the Britain-based watchdog also said.
In a video released by activists from Salqeen, a number of the apparent air strike victims are seen piled in the back of a pick-up truck, their bodies charred black with limbs torn off.
The Observatory also reported shelling in the provinces of Hama, Daraa and Homs.
The group, which collates information from a network of activists and medics on the ground, gave a toll of about 160 people, including 112 civilians, killed in violence across Syria on Monday.
In Aleppo, an AFP correspondent said rebels and regular soldiers traded fierce machinegun fire in and around the historic souk, which reverberated across the centuries-old UNESCO-listed covered market.
The fighting, which took place in an area of the souk facing Aleppo's ancient citadel, came after parts of the market were ravaged by a fire, sparked by fighting, on Friday night and Saturday.
Traders told AFP that the army had no presence inside the souk area, which has been infiltrated by rebels.
The regime and rebels blamed each other for damage to the souk.
"Armed terrorists started the fire in order to cover up for their looting and theft in the market," Aleppo governor Wahid Akkad told an AFP journalist in the city.
However, video posted on YouTube by activists showed rebel fighters trying to put out the fire with a water hose. "We are certain that it was regime fire that started the flames," an anti-regime citizen journalist told AFP.
As the fighting raged, Ban said after a meeting with Syria's Muallem at UN headquarters in New York that it was time for Damascus to lower the scale of its offensive against the insurgency.
"He stressed that it was the Syrian people who were being killed every day and appealed to the government of Syria to show compassion to its own people," a spokesman for the UN secretary general said.
Ban "raised in the strongest terms the continued killings, massive destruction, human rights abuses, and aerial and artillery attacks committed by the government," the spokesman said.
Muallem, meanwhile, addressing the UN General Assembly, said France, Qatar, Saudi Arabia, Turkey and the United States "clearly induce and support terrorism in Syria with money, weapons and foreign fighters."
President Bashar al-Assad was open to reforms if the violence stopped, the foreign minister said. "We still believe in a political solution as an essential way out of the crisis."
For this to happen, he said UN members should press for an end to the "arming, financing, harbouring and training of terrorist groups."
In an interview with Beirut-based Al-Mayadeen TV, Muallem accused the United States of seeking a pretext to attack Syria, comparing the tactic to those that preceded the 2003 US-led invasion of Iraq.
"This issue is an invention of the American administration," Muallem said.
"These chemical weapons in Syria, if they exist - and I emphasise 'if' - how is it possible that we would use them against our own people? It's a joke," he told the staunchly anti-American and anti-Israeli channel.
"It is a myth they invented to launch a campaign against Syria like they did in Iraq," he said.
A US-led coalition invaded Iraq in March 2003, accusing Saddam Hussein of possessing weapons of mass destruction. No such weapons were ever found.
But Ban also warned Syria against using chemical weapons.
"The use of such weapons would be an outrageous crime with dire consequences," he said.
"Chemical weapons simply have no place in the 21st century."
Syria and seven other nations still had not signed the convention, the UN chief noted.
Iran's Foreign Minister Ali Akbar Salehi, also in New York for the UN General Assembly, said Tehran could not support any country - including ally Syria - that used such weapons.
Iran suffered from Iraqi use of chemical weapons during the countries' 1980-1988 war.
Nato chief Anders Fogh Rasmussen said on Monday that Syria's chemical weapon stockpiles were a "great concern" but the solution to the conflict remained political, not military.
At least 30,000 people, including more than 2,000 children, have died in the conflict since it erupted in March 2011, according to figures supplied by the Observatory.