Congress, meanwhile, steered clear of questions whether Digvijay's announcement has caused an embarassment to the party while his son and Madhya Pradesh MLA Jaiwardhan Singh said his father's move to remarry was a "personal matter" and extended full support to him.
"As far as I am concerned, I don't hide my relationship which Mr Modi does. I am absolutely clear in this. I am not a coward which Mr Narendra Modi unfortunately is," the 67-year-old AICC General Secretary told reporters.
In the ongoing Lok Sabha campaign, Digvijay was among the Congress leaders who slammed Modi, who, last month, for the first time publicly acknowledged that he is married.
In his poll affidavit while filing his nomination last month for the Vadodara seat, Modi for the first time made it known that Jashodaben was his wife.
Modi entered his wife's name in a column asking about his marital status. He had left the column blank on previous occasions, including in the last Gujarat Assembly elections in 2012.
At the AICC briefing, Finance Minister P Chidambaram steered clear of questions whether Digvijay's announcement has caused an embarassment to the Congress.
"I do not comment on private life of persons whether belonging to other parties or Congress. It should be best left to the person concerned," he told reporters in Delhi.
Jaiwardhan Singh, a Congress MLA, said his father's decision was a personal matter.
"I think it is a highly personal matter about which I would not like to say anything," he told PTI in Bhopal.
"However, I would like to say that my father has my full support," Singh said.
Digvijay took to Twitter yesterday to announce his relationship with Amrita Rai and plans about marrying her after the social media went viral about it.
"I have no hesitation in accepting my relationship with Amrita Rai. She and her husband have already filed a mutual consent divorce case...Once that is decided we would formalise it," the former Chief Minister of Madhya Pradesh tweeted.