"They were in good condition," said Kitty McKinsey, UNHCR Asia spokeswoman.
"It's a big step forward that we have gotten access to them. We're now getting good co-operation from the Thai government to solve this issue."
She added that she would discuss the UN's findings with the Thai authorities before publicising them but reaffirmed the UNHCR's demand for Thailand not to return them to Burma forcibly.
Many of the 78 people were badly scarred from beatings they said they had received from Burmese troops.
They are being handled by the police and immigration - unlike the Rohingyas who arrived last month and were detained on an island by the Thai military before reportedly being set adrift at sea in barges with no engines and little food or water.
Thai Foreign Minister Kasit Piromya defended the decision to allow the military to investigate.
"Well it's our internal arrangement, and then if the military investigation is not satisfactory we can set up another group to do it," he said.
Senior military officers have previously denied such mistreatment was even possible, and have accused the foreign media of trying to tarnish Thailand's international image.
Our correspondent in Thailand, Jonathan Head, says the issue has been a public relations disaster for the new government - which has been unable to offer a clear response to the international community.
He says that based on previous practice, it is unlikely any military personnel will be held accountable.
The Rohingya are fleeing their home country, where they are denied citizenship by the government.
An unnamed Burmese official told the AFP news agency on Thursday that there was no evidence to suggest the Rohingya were even from his country.
"There is no so-called Rohingya ethnic minority group in our history before or after our independence," he said.
"It is totally unacceptable to say the Rohingya are from Myanmar [Burma]."
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