Russia's President Vladimir Putin told the Ukrainian Paralympic chief that sports events must not be affected by politics, Interfax reports citing the Kremlin.
Ukraine's Paralympic chief said the country would pull out of the Games if Russian troops invade.
"I am very afraid that despite the world's wishes and my call that the irreversible will happen during the Paralympics. I declare: we will pull out of the 11th Paralympic Games in Russia that very second if the thing we fear and which we are against...happens," Valeriy Sushkevich said.
Ukraine's Paralympic chief has asked Russian President Vladimir Putin to ensure peace during the Winter Games.
"I repeated my one request, the one and most important request, that before and during (the Games) there will be peace," Valeriy Sushkevich said.
Channel 4 News presenter Krishnan Guru-Murthy has tweeted:
BREAKING : Ukraine to stay in the Paralympics and raise their flag "for peace" - there will be amazing atmosphere when they walk in tonight
The boot Heather Mills was made to wear to comply with International Paralympic Committee Olympic guidelines caused her "intolerable pain", her management company has said.
The IPC ruled that Mills' new adaptive equipment had not been ratified and she would not be able to compete in the skiing event in 2014 Sochi Paralympic games unless she reverted back to using the approved equipment.
The ex-wife of Paul McCartney subsequently abandoned her plans to compete and withdrew from the selection process - a decision the British Paralympic Association described as "sad".
Mills' management company said the former model was "forced to wear a purely cosmetic, non-relevant full boot cover over her prosthetic leg, adding unnecessary weight and causing intolerable pain", according to the BBC.
The International Paralympic Committee refuted the suggestions and insisted all athletes had to abide by the same rules.
The authority reiterated that only approved adaptive equipment can be used in events.
Heather Mills' alleged outburst left the head of the Paralympic alpine skiing committee "extremely shocked and upset", according to a spokesman for the sporting authority.
"Heather's aggressive behaviour and verbal abuse has left Sylvana [Mestre] extremely shocked and upset," said Craig Spence, the International Paralympic Committee's Director of Communications, in a statement.
"Para-athletes are role models and an inspiration to billions of people around the world. This disgraceful outburst is not what we expect from any athletes competing in our competitions and will not be tolerated."
Mills claims Mestre shouted at her, with her management team accusing the IPC of waging a "vendetta" against her.
The IPC said the incident involving Mills and Mestre was witnessed by a number of people, and insisted Ms Mestre was just trying to enforce the rules and offer the former model a solution to the issue.
"There can be no excuse for such aggressive and intimidating behaviour towards such a highly respected and experienced official within the Paralympic Movement."
The British Paralympic Association has said they were "saddened" by Heather Mills' withdrawal from the selection process for the 2014 Sochi Paralympic game following a dispute with the International Paralympic Committee (IPC) over her adaptive equipment.
The IPC have since accused Mills of "harassing a Paralympic official" after the decision, however the former model's spokesman claimed there was a "vendetta" against her.
In a joint statement, the British Paralympic Association and British Disabled Ski Team said: "The British Disabled Ski Team were informed by IPC Skiing that there was an issue with the adaptive equipment that Heather Mills was using that needed to be addressed before she would be allowed to compete.
"As a result of this and on the back of an injury, Heather Mills has decided to resign from BDST, thereby removing herself from the selection process for the Sochi Paralympic Games.
"Occasionally in sport equipment issues arise, especially with adaptive equipment and the interpretation of the rules in relation to its use.
"Therefore we are all saddened that she has decided to retire at this stage, rather than working with BDST and IPC Skiing to resolve the issue."
Heather Mills won a World Cup silver medal in the women's adaptive slalom event earlier this year in New Zealand.
Mills, who joined the British Disability Skiing team in 2010, also won four gold medals at the US Adaptive Alpine Skiing National Championships last year.
Mills, who had her left leg amputated below the knee following a collision with a police motorbike in 1993, had hoped to compete in the 2014 Sochi Paralympics.
However following a dispute with the International Paralympic Committee over adaptive equipment, Mills withdrew from the selection process.
The behaviour allegedly displayed by Heather Mills "will not be tolerated", the International Paralympic Committee's communications chief has said.
The IPC claim Mills grabbed an official after learning that she would be unable to compete in the alpine skiing event at the 2014 Sochi Paralympics.
Spokesman Craig Spence tweeted the statement with a link to a Daily Express article about the alleged incident.
Mills' team claim there is a "vendetta" against her and that she was shouted at by the official.
The International Paralympic Committee (IPC) has claimed Heather Mills "verbally abused" and physically harassed" an official after learning that she would not be able to compete at the 2014 Sochi Paralympics.
The IPC said Mills, 45, went into a "wild tantrum" after learning that she would not be allowed to participate in the alpine ski competition due to an issue with the adaptive equipment she would have been using, according to the BBC.
"She jumped on me. She grabbed me from the back and she started to say that 'you don't know who I am, I will make your life miserable.'"
However, a statement on behalf of the former model claims Mestre shouted at her after Mills "waited patiently to try and explain...that her left boot was legal and purely cosmetic to abide by the archaic IPC rules."
Mills' coach has claimed there was a "vendetta" against her.