"What we would look for today is … which is which of those countries will express support for the fundamental importance of enforcing the international norm against the use of chemical weapons," Rhodes said.
During the meal, Obama reiterated that the U.S. had intelligence indicating "high confidence" that the Assad regime was responsible for the chemical weapons attack. He appealed to his fellow foreign dignitaries to support a response.
"He reinforced the importance of upholding international norms to which all of the nations here are party to through the Chemical Weapons Convention," Rhodes said.
"He noted the importance of continuing to work through the U.N., but also the paralysis that has existed in the Security Council on the issue of Syria, and therefore, underscored the importance of ensuring that there is enforcement of a norm that is so fundamental to global peace and security."
Rhodes said leaders also discussed resolving the broader Syrian civil war through a diplomatic process.
The White House spokesman also brushed off Russia's attempt to send a delegation of Kremlin-affiliated lawmakers to the U.S. to lobby Congress against a Syrian strike.
"I’d just say that what we’ve repeatedly seen is Russia refusing to take action to hold the Assad regime accountable and seeking to work through different processes to avoid the core issues," Rhodes said. "We can’t have an endless process at the U.N. Security Council that doesn’t lead to anything. Similarly, I don’t know that the Russians have anything to add to the debate in the United States given that we know where Russia stands on this issue. They have continually supported Assad no matter what the facts show, no matter what the regime does."
President Obama apparently did not speak privately with Russian President Vladimir Putin during the dinner, although both leaders spoke to the entire gathering.
Rhodes conceded that Putin's presence, however, kept any sort of consensus on Syria from emerging.
"I don’t think the president ever anticipated that we’d achieve consensus on military action if Russia, for instance, is at the table," Rhodes said.