The group comprised, four Afghans, four Pakistanis, three single Rohingyans; and one Rohingya couple and their three children.
The Refugee Action Coalition said they would be settled in various locations, including Chicago, Las Vegas, Texas and Arizona.
This bring the total number of refugees from Nauru resettled in the US to 155, while just 85 refugees from Papua New Guinea's Manus have so far been accepted into America.
Meanwhile, 23 refugees from Manus bound for the US are still in Port Moresby, since they were transferred there in January
The Coalition's Ian Rintoul said they had been delayed by the need to renew medical clearances and had no idea how long they would have to wait.
About 750 refugees remain on Manus and about a thousand on Nauru where they were detained by Australia five years ago.
No Iranians, Somalis or Sudanese have been accepted for resettlement in the US this year, after US President Donald Trump tried to ban people from the Muslim countries from entering America.
"The [Australian] government's claim that the US deal is going to provide resettlement for the refugees they have kept on Manus and Nauru is less credible by the day," Mr Rintoul said.
"They have admitted that up to 500 refugees will be left behind on Manus and Nauru regardless of the US deal, yet they refuse to accept New Zealand's offer to resettle 150 people," he said.
"It's time the government faced up to the failure of offshore detention and the US resettlement deal. All the refugees and asylum seekers should be brought to safety in Australia."