The threat was made in the presence of senior government officials on the 53rd day of the union's protest demanding appointment letters for its members.
The police said one protester poured petrol on herself and threatened immolation while another put a rope around his neck, the police said.
On the first day of the stir, some people associated with the union climbed to the top of the overhead water tank and have refused to come down, they said.
They threatened to commit suicide, claiming that they would return their homes only after getting appointment letters, they said.
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The officials repeatedly appealed to them to come down and assured them that the state government was considering their case.
"We are here to assure you that your demands would be met soon. You just come down and end your protest," the officials told the agitators.
"Threats and protests are not the right way", the DC said. However, the protesters refused to budge.
Five teachers, Taranjit Kaur, Satnam Singh, Hardeep Singh, Harvinder Singh and Vijay Kumar are atop the tank and have refused to come down despite repeated appeals.
Poonam Rani, the president of the union, said we would end our protest only after getting appointment letters.
"Earlier also, the previous government had befooled us. This time it's 'do or die' for us," said the president, adding even after meeting the education minister five times no decision has been taken..