However, Russia also wants to clear Idlib of groups it considers terrorists, and may still help the Syrian government to do so if a deal fails, as it has done repeatedly since intervening in the war in 2015.
"Even a limited military offensive would displace hundreds of thousands of people", CARE International, the International Rescue Committee (IRC), Mercy Corps and Save the Children said in a statement.
US President Donald Trump cautioned that "the world is watching", as Turkish President Recep Tayyip Erdogan said he feared a "bloodbath".
A day later, its Secretary General Antonio Guterres said that Idlib "must not be transformed into a bloodbath".
The buffer would include parts of Idlib province and the neighbouring regions of Aleppo, Hama and Latakia.
Idlib's other main rebel faction, a Turkish-aligned alliance of groups known as the National Liberation Front, has already expressed its support for the agreement.
But jihadists, who under the deal must withdraw from 15- to 20-kilometre (nine- to 12-mile)-wide buffer zone by Monday, have not yet shown any sign of leaving.
But it later said it was opposed to the deployment of Russian forces in the buffer, and said Ankara promised them that patrols by Moscow would be dropped.
"We can not keep quiet about the continuation of the current situation in Idlib if the Nusra Front refuses to comply with this agreement", Moualem said at a press conference with his Iraqi counterpart Ibrahim al-Jaafari in Damascus.
The biggest threat to the demilitarized zone's success has been the presence of designated terrorist groups such as Hayat Tahrir al-Sham, which evolved from the al Qaeda-affiliated Nusra Front.
Hurras al-Deen has publicly rejected the agreement.
Those fighters also control more than two-thirds of the planned buffer zone and are supposed to withdraw by Monday.
Despite their different positions, rebels and jihadists were reported to have completed the first task of removing heavy arms on time.
HTS, widely considered the most powerful force in Idlib, had quietly abided by the deal's first deadline and re-stationed heavy arms elsewhere. The group also said it "would not forget" the foreign fighters who came to assist it.
On October 10, Turkey announced that the pullout was "complete".
"Get away from the fighters".
Just hours before the cut-off time, Idlib's dominant jihadist group vowed to continue to fight but did not give a clear position on the deal reached in the Russian Federation resort of Sochi.
Late Saturday, "heavy mortar shells" were fired from the planned buffer area into regime territory, killing two soldiers, the Observatory said. "Their fate is sealed and near", one said. "We have not abandoned our choice of jihad and fighting towards implementing our blessed revolution", said HTS.
HTS likely "tried to gain time by neither explicitly refusing nor accepting the deal" between Russian Federation and Turkey, he said.
Other jihadists in the planned buffer zone include the Turkestan Islamic Party and current Al-Qaeda outfit Hurras al-Deen.