Coe, who is standing against Ukrainian pole vault great Sergey Bubka for the presidency of world athletics body IAAF, won his medals at the boycotted Moscow and Los Angeles Olympics of 1980 and 1984.
"I will always oppose boycotts of sport," the London 2012 Olympic chief told Reuters at an event to promote the 10km Great Newham London Run to be held in the Olympic Park in July.
"I don't think they actually achieve what they set out to do. The only people they really damage are competitors and athletes," added Coe, who was on the England committee that bid against Russia for the finals.
"I think it is far better to have sport as a soft power, helping change all sorts of things.
"You either believe in its power to change and to be a catalyst for social and political change or you don't. I happen to believe that sport has done far more to bring communities together than to isolate and separate them."
Ukrainian President Petro Poroshenko posted on Twitter that "while there are Russian forces in Ukraine, I believe that holding the World Cup in that country (Russia) is not possible."
He also told German newspaper Bild that his country's allies should consider a boycott if Moscow failed to pull its troops out of Ukrainian territory.
The IAAF election is in August and Coe has been busy campaigning, visiting four continents in the past two weeks.
He said the most pressing issue was to engage more young people in athletics.
"If the challenge for sport in the 20th century was taking it to communities, the big challenge in the 21st century is taking it to young people," said the Briton.
"And you really do need to recognise that while your sport is athletics...the business is entertainment.
"The biggest challenge we have is to renew our fan base, our audience and make sure that our competitions are relevant to young people."
Newham London Run organisers aim to become Britain's biggest mass participation running event with a target of 60,000 people taking part annually within five years.
The Great North Run is currently the biggest annual running event in Britain with 57,000 participants. The London Marathon attracts roughly 40,000.
(Reporting by Alan Baldwin, editing by Justin Palmer)
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