More than 1,000 migrants have gone ashore in different parts of Indonesia and Thailand, the latest refugees to slip into south-east Asian countries that have made it clear the boat people are not welcome.

Weak, hungry and dehydrated, most of the migrants were crammed on to three boats that Indonesian fisherman towed ashore in Aceh province and North Sumatra, while another 106 were found on a Thai island and taken to the mainland.

Earlier this week, about 1,600 migrants were rescued by the Malaysian and Indonesian navies, but both countries then said they could not accept any more and sent other boats away in what has become a regional humanitarian crisis.

It is not clear whether those who landed today had been turned away earlier.

UN secretary-general Ban Ki-moon said he was "alarmed by reports that some countries may be refusing entry to boats carrying refugees and migrants", according to a statement from his office.

Mr Ban urged governments in the region to "facilitate timely disembarkation and keep their borders and ports open in order to help the vulnerable people who are in need".

South-east Asia for years tried to quietly ignore the plight of Burma's 1.3 million Rohingya but is now being confronted with a dilemma that in many ways it helped create.

In the last three years, more than 120,000 members of the Muslim minority, who are intensely persecuted in Buddhist-majority Burma, have boarded ships to flee to other countries, paying huge sums to human traffickers.

But faced with a regional crackdown, some captains and smugglers have abandoned the ships, leaving many migrants to fend for themselves, according to aid workers and human rights groups. The boats are also filled with Bangladeshis fleeing poverty and seeking better jobs.

Most of the migrants are believed to be heading to Malaysia, a Muslim country that has hosted more than 45,000 Rohingya over the years but now says it cannot accept any more.

Indonesia and Thailand have voiced similar stances, and Thailand is convening a regional conference to discuss the problem later this month.

As boatloads of migrants popped up in scattered spots of south-east Asia's shorelines it was increasingly clear that no one knows how many boats are adrift at sea or where they are.

One of the boats in Indonesia's eastern Aceh province was packed with 790 people, including 61 children and 61 women, many in weak condition from lack of food and water, said Lieutenant Colonel Sunarya, who like many Indonesians uses only one name. Fisherman spotted their vessel on the verge of sinking and towed the boat to the coastal village of Langsa.

"Some of the people told police they were abandoned at sea for days and Malaysian authorities had already turned their boat away," said Lt Col Sunarya, a Langsa police chief who said the migrants came from Burma and Bangladesh.

About 15 miles south of Langsa, fishermen rescued the smaller boat carrying 47 Rohingya, also dehydrated and hungry, said police chief Dicky Sandoni, from Aceh's Tamiang district.

In neighbouring North Sumatra province, fishermen rescued a third boat with 96 people on board, adrift at sea in a motorless boat and weak from hunger, said Captain Suroso of Langkat district police. They were provided basic shelter and food, he said.

Separately, the Thai navy found 106 people, but including 15 women and two children, on a small island off the coast of Phang Nga province, an area known as the Surin Islands and famous for its world-class scuba diving.

"It's not clear how they ended up on the island," said Prayoon Rattanasenee, the Phang Nga provincial governor. The group said they were Rohingya migrants from Burma. "We are in the process of identifying if they were victims of human trafficking." They were taken to the mainland and were being held at a police immigration facility.

Burma, also known as Myanmar, in its first official comments as the crisis escalated over the past two weeks, indicated it would not take back migrants who claim to be Rohingya.

"We cannot say that the migrants are from Myanmar unless we can identify them," said government spokesman Ye Htut. "Most victims of human trafficking claim they are from Myanmar is it is very easy and convenient for them."

Another official, Major Zaw Htay, said Burma "will not attend a regional meeting hosted by Thailand if 'Rohingya' is mentioned on the invitation".

Even the name is taboo in Burma, which calls them Bengalis and insists they are illegal immigrants from Bangladesh, even though Rohingya have lived in the majority-Buddhist country for generations.