Responding to the offer made by China, Ministry of External Affairs spokesperson Gopal Baglay said, "Our stand is absolutely clear".
Asked about Indian national Kulbhushan Jadhav who is in Pakistan custody for alleged espionage, Mr Baglay said, there has been no progress on consular access for Mr Jadhav.
An editorial in the CPI-M journal People's Democracy has also blamed India's growing strategic ties with the United States for the deteriorating relations with China. In the border talks both sides had started working on the possibility of China dropping its claim on Arunachal Pradesh for India allowing it to retain Aksai Chin.
On June 27, China had accused Indian border guards of crossing into its territory from the state of Sikkim on India's northeastern border with Tibet, complicating an already hard relationship.
Mr. Jaishankar told the MPs who attended the three-hour meeting that apart from diplomacy, "other channels" were also being explored to end the standoff and India was insisting that the pre-June 16 condition be reached in Doklam.
Leaders of prominent opposition parties are being invited for the meeting where the two senior ministers will give a detailed presentation on the prevailing situation along the Sino-Indian border and Jammu and Kashmir and the government action, sources said. The Opposition, which has been questioning government's handling of the two issues, will get a chance to raise queries with the government and also offer own suggestions and solutions.
A headline of an opinion piece on Monday in Firstpost, an Indian news portal, noted: "Another war with India will be an economic blunder for China".
"We estimate India now operates seven nuclear-capable systems: two aircraft, four land-based ballistic missiles, and one sea-based ballistic missile", the article said. "India can lend support to Bhutan's position".
The Indian spokesman said the leaders had "a conversation on a range of issues", while a Chinese spokesman maintained no bilateral meeting took place. China was trying to build a road on the land which doesn't come inside its boundary line.
The opposition Congress criticized the BJP Government over the situation in Doklam Plateau, with the party vice-president Rahul Gandhi questioning why Prime Minister Narendra Modi had not yet spoken up on the face-off.