Hassan Wirajuda, the foreign minister, said on Friday that the people are economic migrants and not political asylum seekers.
But according to Human Rights Watch, more than 250,000 Rohingyas fled Myanmar to Bangladesh in 1992 amid a campaign of persecution and what many have labelled "ethnic cleansing" on the part of the government in Naypyidaw.
Wirajuda also said the Indonesian government is working with their countries of origin and the International Organisation for Migration to properly repatriate the migrants.
But it is not clear if they will be sent to Myanmar or Bangladesh.
Shortly after their arrival on Sabang, Imam Husen, one of the migrants, told the Reuters news agency from his hospital bed that he and about 580 other people had set off from Mundu in Myanmar in four boats on December 9 to flee the country.
He said some members of the group had been beaten after landing in Thailand.
They were then towed out to sea and set adrift, he said.
According to Wirajuda, citing accounts by the navy, many died on the trip to Indonesia during which they had to stand because the boat was so full.
Imam Husen's testimony corroborates reports from a Rohingya human-rights group and Indian police reports from other Rohingyas found adrift near the Andaman Islands that Thai security forces towed 992 people out to sea and abandoned them in engine-less boats.
The Arakan Project, a Rohingya non-governmental organisation, estimates that 550 of the 992 are missing, feared drowned.
Colonel Manas Kongpan of the Internal Security Operations Command (Isoc) denied on Tuesday any abuse, saying that all the migrants who arrived in Thailand were sent out to sea with food and water.
The United Nations High Commissioner for Refugees (UNHCR) has asked Thailand for access to 126 Rohingyas it believes are still in custody on a remote island called Koh Sai Daeng.
"[We] welcome the Thai government's willingness to discuss the Rohingya issue on a broad regional basis, because this is a regional issue ... [but] the reason that the Rohingya boat people throw themselves into these small boats and cross the seas on these perilous journeys - the root causes - need to be addressed," Kitty McKinsey, a UNHCR spokeswoman, told Al Jazeera.
|The Thai navy claims it gave the migrants food and water [AFP]
Abhisit Vejjajiva, the Thai prime minister, has promised to investigate the allegations and co-operate with the UNHCR, although the refugee body said on Friday that there has been no formal response to their request from Bangkok.
The Thai prime minister also said any Rohingyas in Thailand would be treated as illegal immigrants and repatriated.
"We have to send them back," Vejjajiva said after chairing a National Security Council meeting.
"We are discussing this, which will require briefing ambassadors of various countries to find a solution."
About 28,000 Rohingyas recognised as refugees are living in UNHCR camps in Bangladesh.