Before meeting Sonia shortly after his return from the United States, Mukherjee told reporters that Chidambaram is a "valuable colleague" and a "pillar of strength."
Chidambaram drove past waiting reporters after meeting Gandhi at her 10, Janpath residence without saying a word.
However, there were media reports that claimed Chidambaram possibly offered to quit in the wake of the controversy.
This was Chidambaram's first meeting with Gandhi, who is also UPA chairperson, after controversy broke out last week over the note to the Prime Minister's Office on the stand taken by him when he was the finance minister.
Details of what transpired at this meeting were not immediately known.
Gandhi met Mukherjee soon after her discussions with Chidambaram. Mukherjee said on arrival that he will speak on the controversial 2G spectrum note only after discussions with Prime Minister Manmohan Singh and other colleagues.
He told reporters at the airport that a full-fledged press conference will be held after the prime minister returns from his visit to New York on Tuesday.
He later told reporters after reaching his North Block office, "If it is needed I will say whatever (I have) to say after Prime Minister comes back and after we have discussions among ourselves."
The March 25 note of the finance ministry suggested that the 2G scam could have been averted had Chidambaram when he held the finance portfolio insisted that the 2G spectrum be auctioned.
The note to the prime minister's office was submitted to the Supreme Court. Union Law Minister Salman Khurshid downplayed the row over the finance ministry note, saying there is no scope for any worry in the document and that inferences drawn out of it were "not correct".
Khurshid also said the note was not worth keeping the media "preoccupied" the for a long time. At the AICC briefing, party spokesperson Rashid Alvi did an apparent balancing act saying neither Chidambaram nor Mukherjee has done anything wrong.
Alvi said the party supported the statement of Khurshid
that even if all parts of the note are believed to be correct, "the inferences drawn are not correct."
Khurshid had also insisted that the note was actually a "summary" and the official concerned had given his opinion over and above the summary in the note.
"People give their opinion over and above the summary. The importance of the opinion will be seen when the issue is discussed," he said.
He also said the note was not worth keeping the media "preoccupied" for a long time. "I have seen the note. I don't think the note has anything on which we should express worry....take it from me this document has no life," Khurshid said, amid a controversy over the stand taken by Chidambaram when he was the finance minister.
"Even if all parts of the note are believed to be correct, I will say that the inferences drawn are not correct," Khurshid said.
Alvi hit out at the BJP for alleging that the embers of the 2G issue will reach the doors of the PMO. "Such type of remarks of BJP are condemnable as the Prime Minister's image is clean and he is a very competent man. I reject all the charges," he said.
Asked whether the Congress was 'exonerating and absolving' the Home Minister in the issue, Alvi said that "I don't think Home Minister has done anything wrong. The matter is pending before court."
"We should wait for the decision. The matter is sub-judice. It is too early to say anything", was his response to a volley of questions.