A police official said security forces launched an offensive to flush them out the militants this morning.
"The exchange of fire between security forces and militants began at around 3.40 am and is going on intermittently," he said.
"Two Army personnel were injured in the gunbattle today," the official said. He said the injured have been taken to a hospital.
The militants had entered into the premises of the DPS Srinagar last evening after carrying out an attack on CRPF personnel deployed on road opening duty near the school.
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Security forces immediately cordoned off the area and launched search operations in the large school campus.
Sources said drone cameras and other hi-tech gadgets were used to trace the location of the militants but police officials refused to comment on operational details.
The authorities have imposed restrictions under section 144 CrPc from Ram Munshibagh to Sempora stretch of the national highway as a precautionary measure to avoid protests near the encounter site.