The group of 93 boatpeople is among about 300 men, women and children being held in crowded conditions at the Phang Nga Immigration Office, north of Phuket.
One of the petitions is written in ballpoint pen in English on a piece of white t-shirt, addressed ''To the Honourable UNHCR and Thailand Government.''
''We want to meet UNHCR,'' it says. ''We demand UNHCR.''
The petition explains that 42 of the 93 boatpeople, who headed for Thailand from the Bangladesh port of Cox's Bazaar, already have refugees cards.
The second petition, seeking a reunion with family members, is addressed ''To the Honourable Muslim Committee, Our prayer for to meet our family.''
It is believed efforts will be made to pass on the petitions to the UNHCR in Thailand and to senior members of Thailand's Muslim community.
Both petitions have been seen and photographed by Phuketwan. Images of the petitions accompany this article.
A Human Rights delegation of officials from Bangkok was allowed brief access to see conditions in the Phang Nga Immigration centre and to interview five of the captive Rohingya yesterday.
Although the petitions appear to have come from a group of boatpeople who departed from Cox's Bazaar, it is believed most of the recent arrivals in Thailand have come from Sittwe, a township in troubled Rakhine state, also known as Arakan.
The arrival of women and children on boats that in recent years only carried men and boys has confirmed fears that levels of desperation among Burma's oppressed Rohingya Muslim minority have grown amid ethnic cleansing and the torching of homes.
Although largely unreported, the Rohingya in Rakhine are said to stll be confined to camps or villages, suffering hunger and deprived of health care and the ability to earn a living.
New arrivals in Thailand have spoken of their desire to reach ''a third country'' and not to be returned to Burma.
The two petitions that appeared on Phuket last night are believed to have been smuggled out of the Phang Nga Immigration centre without the knowledge of most of the visiting delegation.
Originally, the boat from Cox's Bazaar contained 96 people but three of the menfolk - the organisers of the voyage - absconded while the group was being held in an open camp in the Phang Nga port of Kuraburi.
The men were quickly recaptured by local police. Officers reportedly rejected offers of large bribes to allow the men to stay free in Thailand.
It is believed the men were given a stern lecture about the potential for their actions to endanger the well-being of the whole group.
Some of the women and children among the large group being held at Phang Nga were believed to be moving to other holding centres last night or today.
The Phang Nga Immigration centre is thought to have a realistic capacity of less than 100 detainees.
Some of the captives are also likely to be moved to the northern provinces of Thailand - a prospect that is likely to further fragment Rohingya community groups and to split families.
Thai authorities have said they will hold the boatpeople and other Rohingya freed from transit traffickers' camps along the Thai-Malaysia border for up to six months while their futures are decided.
The Foreign Ministry has promised in-principle access to the UNHCR, the United Nations body that oversees all refugee issues, but details have yet to be agreed.
To the Honourable UNHCR and Thailand Government
Sub: Prayer for Refugees
Sir or Madam
We are Rohingya refugees in Bangladesh. We want to meet UNHCR. We demand UNHCR. We are two group. One Group is registered refugees. Another group is unregistered refugees.
Registered refugees have card. Unregistered refugees have no card. We are 93 persons. Refugee 42 persons are registered refugee 51 persons are unregistered refugee.
Venue: We hope that to accept our petition. It is more kindness for us: New Cottage Road 4700 Cox's Bazaar.
To the Honourable Muslim Committee
Our prayer for to meet our family
Sir and madam
With due respect and humble submission we most respectfully to start that we are sorrowfully men under your Thailand Government.
Sir We hope that to your mouth saying to left in prison. also we live here 15th days ago, in the prison. Here is most group. They group between 3 group gone to another place but we are not move to another place. Now we are staying in the prison. Also we wanted to meet our family. If you would kindly to meet family. It is very grateful to us. After we are not to know where to live our family.
Venue: We hope that to accept our petition. You would be kind enough to as as soon as you possibility.
Yours sincerely (unintelligible) Rotigue No. 215.