Lavrov, visiting Cairo, said his government supported a draft resolution backed by the United States, the news agency RIA Novosti reported.
"[A] version with the amendments was distributed literally at the last moment, when we were about to depart from Geneva," he was quoted as saying.
He didn't say which country proposed the changes.
U.S. Secretary of State John Kerry said multilateral negotiators were very close to reaching a deal with the Iranians. He said Thursday in an interview on MSNBC's "Morning Joe" the U.S. government was considering laying off "a tiny portion" of the sanctions on Iran as a bargaining chip.
"Ninety-five percent or more of the current sanctions will remain in place," he said.
U.S. State Department spokeswoman Jen Psaki said Wednesday the United States, Russia, China, the United Kingdom, France and Germany -- the so-called P5+1 -- were united last week and there "was a moment where Iran couldn't accept the deal as offered."
Alaeddin Boroujerdi, chairman of the National Security and Foreign Policy Commission in the Iranian Parliament, said Western powers were the ones who failed to show unity at the negotiating table, Iran's semiofficial Fars News Agency reported Thursday.
Iran is accused of pursuing the technology needed to manufacture a nuclear weapon, an allegation it denies.
A second round of talks is scheduled Wednesday in Geneva.