"I wish the organisers of what is happening in Jammu would take up our offer and fly over the (Amaranth) route in the state chopper to see extent of snow," he wrote on micro-blogging site Twitter.
The chief minister said the protesters, however, would not accept the offer as they can't face the truth.
"But of course they won't because the truth is inconvenient, as is acceptance of the fact that yatra dates were set by Sri Sri Ravishanker ji," he tweeted.
Responding to a tweet about state government stopping the pilgrims from embarking on the religious journey, Omar said weather is favourable so as to start the pilgrimage right now.
"Actually, right now God is stopping you because there is so much snow on the route that it is not possible to move on the route," he wrote.
A large number of Amarnath pilgrims, who tried to proceed towards the cave shrine from Jammu ahead of the scheduled date, were held yesterday.
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Shri Amarnath Shrine Board (SASB), which manages the annual pilgrimage, has fixed June 25 for the start of the yatra, which will conclude on August 2.
Several right-wing groups were demanding that the government extend the duration of the yatra to two months starting from June 4, coinciding with the occasion of 'Jayeshth Purnima'.
They accused the government and SASB of deliberately trying to curtail the period of the pilgrimage at the "behest of separatist forces".