The two leaders were seated on either side of Gandhi at the foundation stone laying function of PGIMER's Satellite Centre at Ghabdaan here.
In April this year, former Chief Minister Amarinder Singh was removed from the post of state Congress chief and replaced with Bajwa, fuelling an internal rivalry within the party.
Amarinder who spoke first at the function, chose to give Bajwa's name a miss, but was immediately reminded by local MP Vijay Inder Singla.
Stressing that there were only six months left for the Lok Sabha polls, he said, "We need to put the opposition on the mat. We will teach them a lesson when we come to power."
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He also slammed Badal, who had been miffed over "not being invited" for the function.
"I also served as PCC chief for seven years, but Badal never invited me for any official function," Amarinder said.
Taking over the microphone, Bajwa remarked that "my elder brother may forget my name, but I cannot do so", in an open jibe at Amarinder.
"First, we need to be united and then we can form the government," Bajwa said, adding that only after being united we can decide "on who needs to be thrashed and put on mat".
Throughout the function, both the leaders did not talk to each other.
The occasion, organised by Singla, saw the attendance of Union Ministers Ghulam Nabi Azad, Manish Tewari, Santosh Chaudhry, Congress general secretary Shakeel Ahmed among others.