In a statement issued from the Syrian capital, where the team arrived earlier this week, the UN said the experts hoped to have a comprehensive report ready "by late October".
The UN mission is separate from a team of Organization for the Prohibition of Chemical Weapons inspectors due to get to work by next week in Syria destroying its chemical arsenal.
The alleged attacks being investigated include a March 19 incident in Khan al-Assal, in northern Aleppo province, which both the government and foreign backed militants reported, each accusing the other side of responsibility.
Other sites that will be investigated include the Sheikh Maqsud neighbourhood in Aleppo city, allegedly the site of an April attack, and Saraqeb in northwestern Idlib province.
The team is also continuing investigations into an August 21 attack in the Ghouta area in the suburbs of Damascus, which occurred during their group's first mission to Syria last month.
The experts visited the site of that alleged attack during their first trip and issued a preliminary report earlier this month confirming the use of the chemical weapon sarin there.
In addition, the team is investigating an alleged attack on August 22 in the Jubar district of Damascus, and a seventh incident reported in Ashrafiyeh Sahnaya in Damascus province on August 25.
"The UN team of investigators, which returned to Syria for a second working visit on 25th September, expects to finalize its activities in the country by Monday, 30th September," the statement said.
"In the course of performing their task, the experts have received several documents and samples and have conducted many interviews."
The statement said the team was working on a "comprehensive report that it hopes will be ready by late October".
The team's first report, issued on September 16, said there was evidence that the nerve agent sarin had been used in the August 21 attack.
But the experts are mandated only to investigate whether chemical weapons were used, not to determine who was responsible for their use.
The militants operating inside Syria and the foreign-backed Syrian opposition claim that the Syrian army carried out the fatal attack in August. However, Damascus strongly rejects the allegation and says the militants carried out the assault to draw in foreign intervention.
NJF/NJF