Russian diplomats felt that the talks would not be constructive after Belarus was raised at a separate UN meeting on Ivory Coast and Lebanon.
William Brencick, the US envoy, raised a hunger strike by a jailed opposition politician in Belarus, prompting an angry response from Russia's UN ambassador.
Vitaly Churkin said the issue had nothing to do with the council's business and showed anything can be raised in the 15-member body.
Meanwhile, Wang Guangya, China's UN ambassador who showed up for a separate Iran meeting among six key nations, told reporters that he had complained the session on a resolution imposing sanctions on Tehran had been rescheduled three times.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
"So I asked for some respect," Wang said. "Then our colleague from Russia joined and said he would get instructions on the issue" of Belarus. Then everyone left, Wang said.
Emyr Jones Parry, Britain's UN ambassador, said: "It wasn't the best timing by the US."
Britain, France and Germany have revised a resolution backed by the United States that would impose sanctions on materials and technology that could be used in nuclear weapons, uranium reprocessing work and heavy-water reactors.
But Russia, which has veto power on the council, still objects to a travel ban and a freeze of assets of leading Iranian agencies, businesses and people involved in the country's nuclear programme.
On Belarus, the United States raised the plight of Alexander Kozulin, one of two opposition figures to run against Alexander Lukashenko in his successful presidential re-election campaign in March.
He was jailed for five-and-a-half years for organising rallies after official results gave the president a landslide victory. Kozulin ended a 53-day hunger strike on Tuesday.
"This highlights the situation in Belarus, concerning the lack of democracy in the heart of Europe," a US official said, speaking on condition of anonymity.
"We have never shied away from raising issues of fundamental freedom and political expression."