Leaders of 11 political parties, including JD-S leader and former prime minister H D Deve Gowda, and CPI's D Raja, were briefed by External Affairs Minister Sushma Swaraj, Defence Minister Arun Jaitley, Foreign Secretary S Jaishankar and Home Secretary-designate Rajiv Gauba, on the two issues.
Opposition leaders were told about the prevailing situation along the Sino-Indian border and Jammu and Kashmir and the government's action, an official spokesperson said.
"Those who were absent in yesterday's meeting were invited for today's meeting," an official spokesperson said.
Representatives of JD-S, CPI, RSP, JMM, Sikkim Democratic Front, partner of ruling NDA Akali Dal, besides others, were present in the meeting.
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Congress, TMC, CPI-M, JD-U, DMK, BSP, NCP and others had attended yesterday's meeting.
CPI national secretary Raja said the government told them there are differences on Dokalam area in the tri-junction of India, China and Bhutan.
"The government said there is no tension and it is negotiating. I also said the standoff should be brought to an end as early as possible through the already existing mechanism," he told PTI.
"The government gave details about the attack on Amarnath pilgrims. We did not discuss the Kashmir issue as a whole, but only the Amarnath attack issue," he said.
Gauba briefed the leaders of the 11 parties on the Amarnath pilgrimage this year and said till yesterday l.86 lakh pilgrims had paid obeisance at the cave shrine.
Last year, 2.21 lakh pilgrims had visited the shrine during the entire yatra period.
The security arrangements have been reviewed regularly at the Centre and the state level, he said.
New Delhi has expressed concern over Beijing trying to change the status quo at the India-Bhutan-China tri-junction in the Dokalam area.
China and India have been engaged in a standoff in the Dokalam area for the past three weeks after a Chinese military construction party attempted to build a road.
Doka La is the Indian name for the region which Bhutan recognises as Dokalam, while China claims it as part of its Donglang region.
Four districts of the state -- Pulwama, Kulgam, Shopian and Anantnag -- have been on the boil since the killing of Hizbul Mujahideen commander Burhan Wani in an encounter with security forces in July, 2016.
The unrest has resumed since the April 9 bypoll to the Srinagar Lok Sabha seat.
Opposition leaders have been criticising the government for the way it has handled China and Kashmir.