Women and children outnumber the menfolk among the three illegal immigrant groups detected and detained in Thailand so far, totalling about 410 people.
The allegation that the travellers are ''terrorists'' comes today in a news report in a national English-language newspaper, quoting an unnamed police source.
''The groups in question are composed of significant numbers of small children, and more than a few pregnant women,'' Phil Robertson, Deputy Director, Asia Division, Human Rights Watch, said today, ''so one wonders how unnamed police sources have suddenly somehow jumped to a conclusion that these people are 'terrorists.'''
The claim attributed to the anonymous policeman could disturb sensitive investigations now taking place involving three countries - Thailand, Turkey and China - about the status and future of the families.
No evidence has been made public so far to support the claim that the mysterious new arrivals are terrorists, but there is substantial evidence that they are terrified.
For 48 hours, the first group detected in the Thailand jungle remained silent, except for a lone spokesperson, as women hid the faces of their children from the media in a parking lot at Had Yai's Immigration 6 headquarters.
The arrival of several Turkish envoys and a man from Istanbul who had flown to Thailand to help brought tears of relief, even among the men.
Caucasian in appearance, the families are claiming Turkish ethnicity. Some say they are seeking to migrate to Australia. Other say Turkey is their destination.
But there is also a suspicion that many are Uighurs, fleeing intense persecution of the Muslim minority in China's Xinjiang province.
Thai authorities sometimes concoct theories about ''terrorists'' in an attempt to relieve themselves of the requirement to show consideration for unwelcome immigrants, or to divert attention from the lack of scrutiny on porous borders.
Back in 2009, when an increase in the number of Rohingya led Thailand to adopt the inhumane ''pushbacks'' policy, the boatpeople fleeing ethnic cleansing in Burma were also labelled as potential terrorists.
No connection was ever found. At that stage, the Rohingya were all men and boys. Allegations now being made about the mysterious families, including pregnant women and toddlers, come as no surprise to Human Rights Watch.
''It seems pretty clear that Thai officials have some ulterior motives in trying to tar this entire group with the 'terrorist' label,'' Mr Robertson said.
''In fact, such allegations sound surprisingly like those regularly made by Chinese government security officials, whose motives are hardly pure since they are precisely the ones responsible for the abuses that the Uighurs are fleeing from in their Xinjiang homeland.''
Turkish officials have been heavily involved in determining the status and future of the new arrivals so far with documents sent to Turkey for assessment. ''It's a humanitarian issue,'' one envoy told Phuketwan reporters earlier this month.
''I suspect that such 'terrorist' accusations are a prelude to some Thai government officials trying to force these groups back to China in what would be a clear violation of international law,'' Mr Robertson said.
''It is time for the UNHCR and the international community to clearly tell Bangkok that such an outcome would be totally unacceptable.''
Discovery of the new wave of illegal immigrants over little more than a week has led to claims that the network of human trafficking established with official connivance to deal with thousands of Rohingya is now so sophisticated and lucrative that its organisers are encouraging other oppressed groups to flee through Thailand.
At present, 115 male adults among the mysterious new arrivals are being held with 447 Rohingya by Immigration officials near the Thai-Malaysia border in Pedang Besar and Sadao.
Woman and children are being held in a family shelter in Songkhla province. A third group detained in Sa Kaew province near the Thai-Cambodia border have been taken to the central Immigration Detention Center in Bangkok.
Sources in Thailand's south tell Phuketwan reporters there may have been two other groups detected, and that hundreds of Rohingya and mysterious families are still being held in secret jungle camps.