In a rare move, the Army chief briefed the Senate - the upper house of the parliament - on security situation and regional issues on Tuesday.
During the briefing, Gen Bajwa supported the peace talks with India, the BBC Urdu reported.
"We can resolve issues with India through talks instead of war. In this situation if the government decides to hold talks with India, then the army would back the government," he was quoted as saying.
"We want good ties with all neighbours including India and Afghanistan," he told the Senators.
More From This Section
The powerful army, which enjoys considerable influence over policy decisions in Pakistan, has ruled the country for much of its life since it gained independence 70 years ago.
Gen Bajwa was accompanied by Director General of Military Operations Maj Gen Sahir Shamshad Mirza, Director General Inter-Services Intelligence (ISI) Naveed Mukhtar and Director General Inter-Services Public Relations Maj Gen Asif Ghafoor.
It was for the first time in six years that the military leadership had come to the Parliament House to brief lawmakers on the security situation.
Officials provided only limited information about the four-hour meeting between Gen Bajwa and lawmakers but the media reported the details of the discussion quoting senators.
Senate chairman Raza Rabbani criticised lawmakers for leaking details of the in-camera briefing by the Army chief, saying they had violated the sanctity of the upper house.
He added that senators should know that in-camera sessions are not spoken about in the public.
Rabbani forwarded the matter to the House Business Advisory Committee for breaching the privilege of the Senate.
He tasked the committee, which will include leaders of the house and opposition in Senate and parliamentary leaders of all political parties, to investigate the matter and devise a strategy for future in-camera sessions to prevent similar situations.