Russia, hosts of the 2014 Winter Olympics in the Black Sea resort of Sochi, passed the controversial law in June.
Critics have said it effectively disallows all gay rights rallies and could be used to prosecute anyone voicing support for homosexuals.
President Vladimir Putin also banned same-sex couples from adopting children.
"We should use all the avenues possible for influence and diplomacy with Russian officials, so that this legislation will not create a problem for our athletes," Carrion, one of six candidates for the IOC top job, said in a statement on Friday.
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"I am confident that the discussions going on now with the Russian authorities will help clarify the extent of the law and will ensure that our athletes will be protected," he added.
Russian sports minister Vitaly Mutko said on Thursday foreign athletes or spectators found breaking the law would "be held accountable".
Puerto Rican banker Carrion, who heads the IOC's finance commission and is also a chief negotiator for the Games broadcast rights, said the absence of discriminatory laws should be a condition for future Games candidates.
"Looking ahead, a condition to getting the Olympic Games in the future should be to make sure the city does not have laws that discriminate against people in anyway, consistent with the Olympic Charter," he said.
"I strongly believe in equal rights, including the right to practice sport, for every human regardless of race, nationality, gender or sexual orientation.
"The Olympic Games celebrate humanity through respect, friendship and excellence. One of the deepest core values of the Olympic Movement is 'sports as a human right.' Nothing should ever stand in the way of that," he said.
The law has triggered a boycott of Russian vodka in parts of the United States as well as calls for an overall Games boycott.
Putin, who denies clamping down on political opponents, has made Sochi a top priority for Russia to help its image abroad by propagating it as a modern state with top-notch infrastructure.
But the latest controversy only adds to criticism over cost overruns and accusations of widespread corruption marring the February 7-23 Games.
(Reporting by Karolos Grohmann; editing by Toby Davis)
