"We come here not only for sport," he told reporters on Wednesday.
"Of course it's our first job but every day in my country, people die, animals die, buildings are broken - sport buildings, civilian buildings.
"It's not possible to explain to you what's happening, you need to come to understand."
President Volodymyr Zelenskiy on Wednesday said that the very fact that Ukraine was participating in the Olympics was an accomplishment in wartime.
Ukraine is fielding its smallest ever Summer Olympic team of about 140 athletes and the country has lobbied hard to ensure athletes from Russia and from Belarus, the Kremlin's close ally, were barred from taking part in Paris.
The war has claimed the lives of thousands of Ukrainians including at least 488 athletes according to the country's sports ministry.
"When people tell me it's about sport, it's not politics, no, sorry, I don't agree with this," Verniaiev said.
A Russian missile all but destroyed sections of Ukraine's largest children's hospital in Kyiv on July 8, a site Verniaiev and his team visited.
"How can you think about sport, about gymnastics, about competition when you see news like this," he said.
"But of course we do our job to the maximum with what we have."
The Kremlin, without providing evidence, said it was Ukrainian anti-missile fire, not Russia, that hit the children's hospital earlier this month. Russia denies that their armed forces have intentionally targeted civilians in Ukraine.
Gymnastics will run from July 27 to August 5, with the men's team final on July 29.