But US Ambassador Nikki Haley said the "world must see justice done", referring to Moscow as the "Russian regime, whose hands are all covered in the blood of Syrian children".
Diplomats said the US was pushing for a vote on Tuesday on its draft resolution setting up a Syria gas attacks inquiry, but Russia could veto the measure.
Russia vetoed in November a Western-backed resolution extending the mandate of the Joint Investigative Mechanism (JIM), which on several occasions had previously found the Syrian regime culpable for launching chemical weapons attacks.
Nebenzia said the new US draft "contains some unacceptable elements which may make it even worse".
On Tuesday, a senior Russian lawmaker said Moscow is willing to help arrange a visit this week for experts from the Organisation for the Prohibition of Chemical Weapons (OPCW) to inspect the site of the alleged chemical attack.
Yevgeny Serberennikov, from the defense committee at the Federation Council, told the RIA Novosti news agency that Russia is anxious for the OPCW to "finally start carrying out the functions it was created for".
Russia's offer comes as President Donald Trump is threatening an imminent military strike against Syria.
Trump slammed the "horrible attack" and vowed to respond "forcefully". "We're going to make a decision tonight or very shortly thereafter," he told reporters.
Medical groups and rescuers said at least 49 people died after Saturday's suspected chemical attack in Eastern Ghouta.
Access to Douma, the largest town in Eastern Ghouta where the alleged chemical attack took place, has been limited. Inspectors and news agencies have been blocked from independently verifying the accounts.
In April last year, Trump launched a cruise missile strike against a Syrian air base within 72 hours of the Khan Sheikhoun chemical weapons attack the JIM later pinned on the Syrian regime.
But any new action against the Syrian regime risks open conflict with Russia which, like Iran, has deployed forces to defend their ally President Bashar al-Assad.
Earlier, Trump was asked whether Putin bore some of the responsibility for the latest attack. "Everybody is going to pay a price. He will. Everybody will," the American president warned.
The OPCW said it was investigating the Douma attack allegations, but that so far only a "preliminary analysis" had taken place.
The Syrian regime launched an offensive against Eastern Ghouta on February 18 that has left more than 1,700 dead and forced tens of thousands from their homes.
Agencies contributed to this report.
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