After a tip-off, 114 people were rounded up in the southern province of Songkhla on Thursday, but some were freed because they were able to present valid travel documents.
"The 61 were arrested and charged for overstaying their visas, illegal entry or not going through proper channels," said Colonel Phutthipong Musikkul, commander of Songkhla immigration police.
"It's likely that these people wanted to go to a third country," Phutthipong said, without elaborating.
Earlier this month Thai authorities said they were holding for possible deportation 128 Tamil migrants arrested in Bangkok, including some who had registered with the United Nations as asylum seekers.
Some reports suggested they hoped to travel to Canada, whose government welcomed news of their arrest.
Almost 500 Tamil refugees arrived in Canada in August aboard a cargo ship which reportedly spent 90 days traveling from Thailand before police boarded it in Canadian waters and piloted it ashore in western Canada.
Sri Lan