Unidentified attackers fired at a UN convoy as it tried to approach Ghouta, east of Damascus, hitting the tires and front window of the lead vehicle, said a UN spokesman, Farhan Haq.
The team made a new attempt to reach the scene of last week's attack, in which hundreds of people are said to have died, and visited two hospitals, Haq added.
"It was a very productive day and once (the team) has made its evaluations it does intend to continue its work tomorrow," the spokesman told reporters.
The team, led by Swedish expert Ake Sellstrom, is "already gathering valuable evidence," said the spokesman.
UN leader Ban Ki-moon said that despite the "very dangerous circumstances", the investigators "visited two hospitals, they interviewed witnesses, survivors and doctors, they also collected some samples."
According to UN officials, the hospitals are in the Moadamiyet al-Sham district near Damascus.
The UN team was in a buffer zone between government and opposition-held areas when it came under attack.
Ban said the United Nations had made a "strong complaint" to the Syrian government and opposition forces, and demanded that the safety of the UN experts be guaranteed.
The rebels and President Bashar al-Assad's government have blamed each other for the sniper assault as they have also traded accusations over the launch of the chemical attack.
Western nations have accused Assad's forces of using chemical weapons, which are banned under international law. The August 21 attack at Ghouta has led to heightened speculation that a military strike could be launched against government targets.
Diplomats said however that the presence of the UN inspectors in Syria could complicate any military plans.
The 13 UN inspectors and seven translators and backup staff arrived in Syria on August 18 to start an investigation into whether chemical weapons have been used in the 29-month old conflict that has left more than 100,000 dead.
The inspectors' mandate is only to find whether chemical weapons have been used in the war.
But Haq said the team "will complete a scientific analysis as soon as possible and the mission will seek to reconstruct an evidence-based narrative of alleged incidents and other information in accordance with these guidelines."
Diplomats said the comments indicated that any report by Sellstrom could at least give a pointer as to who was behind the attacks.
The team was sent to Syria to investigate reports of a chemical weapons attack near Aleppo in March and at two other locations. But the August 21 assault at Ghouta is now the "priority," said the UN spokesman.