"No one can be forced to flee, by any specific route or to any particular location," said O'Brien.
"Protection must be guaranteed for all according to the principles of neutrality and impartiality."
Government forces have surrounded rebel-held districts in eastern Aleppo since July 17, sparking fears for an estimated 250,000 people who live there.
Residents have reported food shortages and spiralling prices in rebel districts since regime forces cut off the opposition's main supply route into the northern city earlier this month.
Russian Defence Minister Sergei Shoigu said three humanitarian corridors were being opened "to aid civilians held hostage by terrorists and for fighters wishing to lay down their arms".
He told Russian news agencies that a fourth corridor would be opened to the north of Aleppo for rebels to flee with their weapons.
Medical and food assistance would be provided along the routes for civilians and fighters who lay down their weapons, Shoigu said.
President Bashar al-Assad, meanwhile, issued a decree offering an amnesty to rebels who surrender over the next three months, state news agency SANA reported.
"Everyone carrying arms... and sought by justice... is excluded from full punishment if they hand themselves in and lay down their weapons," it said.
Syria's state television also announced "the opening of three passages to allow citizens out of eastern districts" of Aleppo.
Regime planes on Thursday dropped flyers showing a map with the location of these humanitarian passages, he said, as well as small aid packages, an AFP correspondent said.
He went to see one of the corridors but said it remained closed and saw no movement of local residents nearby.
"We're scared of using the regime crossings because we refused to do military service. The corridors are nothing more than words. It's just an excuse to throw people into jail," said Hassan Ibrahim, a 25-year-old father.
- Regime advance -
Previously the country's economic hub, Aleppo and its surrounding countryside have suffered some of the worst fighting in the five-year conflict that has killed more than 280,000 people.
It has been roughly divided into a regime-controlled west and a rebel-held east since July 2012.
Analysts say that losing Aleppo would be a major blow for the armed opposition and could signal a turning point in the conflict, which began in 2011 with the brutal crackdown of anti-government protests.
Also on Thursday, Syrian government forces drove rebels from the neighbourhood of Bani Zeid, on Aleppo's northern outskirts, after heavy overnight fighting, a monitor said.
The Syrian opposition High Negotiations Committee condemned Russia’s proposal as "a euphemism for Russia’s efforts to alter Aleppo’s demographics and ensure forced displacement".
"The forcible displacement of Aleppo’s population is a war crime perpetrated by the Syrian regime and a permanent member of the (UN) Security Council," it said, referring to Russia.
Amnesty was also dismissive.
The Russian plan was "not a substitute for allowing impartial humanitarian relief for civilians who remain in opposition-held areas of the city or other besieged areas, many of whom will be sceptical about government promises", it said.
UN envoy Staffan de Mistura said the world body had not been consulted on Russia's initiative.
Meanwhile, Human Rights Watch accused Assad's regime and Russia of extensively using banned cluster munitions against the rebels since late May.
The New York-based watchdog said it had documented 47 cluster munition attacks that killed and injured dozens of civilians in rebel-held areas in three provinces since May 27, many north and west of Aleppo.
On the opposition front, the Syrian branch of Al-Qaeda, Al-Nusra Front, announced Thursday it was breaking ties with the global terror network.
Al-Nusra is a main rival of the Islamic State jihadist group from which it wants to distance itself as a target of foreign air strikes.
At least 15 civilians were killed and dozens wounded Thursday in US-led coalition air strikes on the northern IS-controlled town of Ghandoura, said the Syrian Observatory for Human Rights.
The town is near Manbij, a strategic waypoint between Turkey and the IS bastion of Raqa, and came after the coalition opened a formal investigation to determine whether its air strikes last week near Manbij claimed dozens of civilian lives.