AICC Secretaries Harish Chowdhary, Naseeb Singh, Prakash Joshi and Shakeel Ahmed Khan had a meeting with Dwivedi, who is party's General Secretary in-charge of organisation.
Sources said the young leaders apprised Dwivedi of their concerns.
On a visit to his Lok Sabha constituency Amethi, Gandhi told reporters there that "there are multiple voices in Congress party" and all these voices will bring solution to it.
"There are always these types of tension and we will deal with it," the Congress Vice President said when his comments were sought about the infighting in the party after it suffered a rout in the Lok Sabha elections.
Coming out against the old guard and in support of Rahul, 16 young Congress leaders have decided to write to seniors against damaging the party's image and making controversial statements outside party fora.
The move comes days after Dwivedi and another party general secretary Digvijay Singh had made remarks that included prescribing an age limit for holding active posts and concluding that Rahul should be seen more active in politics. The remarks, the young leaders feel, have damaged the party's interests and image.
After holding a second meeting yesterday, Prakash Joshi, picked up by Rahul, told PTI "all those leaders giving public statements should first introspect how far they discharged the responsibility that was given to them".
He said "what is wrong if Rahulji wants to involve the voice of workers in decision making. We are fully with him even if he has to take some hard measures".
On Tuesday night, a group of secretaries were huddled in a meeting outside AICC office to discuss the controversial remarks made by a number of party leaders ever since the worst-ever poll debacle of Congress in the general elections.