CNRP lawmakers say recently approved amendments are unconstitutional.
Authorities prosecute, detain, and harass activists to silence dissenting voices, the groups say in an open letter.
Local officials say as many as 40,000 Rohingya arrived during the past three days.
Activists call for growing pressure on Beijing over Tibet, and over its pursuit of its critics, Chinese and foreign, far beyond its borders.
The call to residents to surrender to police breaks authorities' earlier pledge not to pursue charges against them.
The parliamentary vote was approved without debate in a session boycotted by all 55 CNRP lawmakers.
Foreign ministers urge government to allow humanitarian access for NGOS and say Myanmar should cooperate with UN rights inquiry.
But Chinese travelers and trade goods cross without delays, a local source says.
Factories are being shut down in a bid to clear the skies, while outspoken critics of the government have been placed under close surveillance or sent on forced "vacations."
They take on tough farm work to make up for wages lost by men held in re-education camps.
The crackdown comes after the Xinjiang Communist Party chief calls for a massive region-wide security operation to prevent the occurrence of any incident, large or small.
An official says detainees will not be freed until they admit it was ‘wrong’ to leave China.