The boat carrying at least 100 refugees was intercepted by Indonesian authorities after it ran into trouble off the coast of the Aceh province.
Indonesia is sending a boat with dozens of Rohingya refugees into Malaysian waters.
Authorities said on Tuesday that at least 100 mostly women and children aboard a wooden vessel were denied refuge in Indonesia and instead pushed into the neighbouring Southeast Asian country.
The boat was intercepted by Indonesian authorities after it ran into trouble off the coast of the Aceh province.
Despite calls from non-governmental organisations and the United Nations agency for refugees, Indonesian authorities are attempting to send the group back after providing supplies, clothes and fuel, as well as a technician to fix their damaged boat.
"We hope (the supplies) can help the Rohingyas to continue their journey to Malaysia as they planned and intended," Winardy, an Aceh police spokesperson who, like many Indonesians, goes by only one name, told AFP new agency.
"We will monitor them until they reach their destination," he said.
The wooden boat was first sighted two days ago, stranded about 70 nautical miles off the Indonesian coast, according to a local navy commander.
"This is about life and death"
Indonesian authorities have not pushed back Rohingya refugees as strongly as Malaysia or Thailand, instead reluctantly accepting them upon arrival by sea.
But Amnesty International and the UNHCR have called on the government to let the stranded group of Rohingya refugees land.
"This is about life and death. There are women and children, we must pay attention to their health," executive director of Amnesty International Indonesia Usman Hamid said in a statement.
The UNHCR also called on Jakarta to let the boat's passengers disembark, pointing to the unseaworthiness of the boat.
Badruddin Yunus, a leader of the local fishing community, told AFP that fishermen who had visited the boat reported there were 120 people on board, including 51 children and 60 women.
He said the engine was broken and the refugees could not communicate with the local fishermen due to the language barrier.
Last year, hundreds of Rohingya who fled persecution in Buddhist-majority Myanmar arrived in Indonesia.
Many have since escaped to Malaysia, drawn by its substantial population of more than 100,000 Rohingya.