Railway Minister Pawan Kumar Bansal was seen feeding a goat on Friday, which was reportedly sacrificed later. Many believe that it wards off bad luck and is a widespread practice.
Bansal is under a cloud over his nephew's alleged involvement in bribery for a plum railway board posting.
Vijay Singla, Bansal's nephew, was caught in Chandigarh with the bribe money of Rs 90 lakh and arrested by the CBI.
Bansal, who also skipped the cabinet meeting Thursday, is under pressure following the arrest of his nephew Vijay Singla by the Central Bureau of Investigation (CBI) in connection with his alleged acceptance of Rs.90 lakh as part-payment of a bribe for the promotion of an official to the Railway Board.
Law Minister Ashwani Kumar is also facing the heat from the opposition over accusations that he vetted - and changed - the draft CBI report on the coal blocks allocation controversy.
Sources said there is unease in the Congress over the controversies surrounding the two ministers, and a meeting of the core group was expected Saturday.
They said the core group could also informally meet Friday to take stock of the situation.
Party sources said Bansal's continuation in office would become untenable if the CBI decides to question him in the bribery case over the railway posting.
They said CBI investigators seem to be closing in on the minister.
"It would be embarrassing for the party if he were to be quizzed," a party leader said.
Sources said the party was looking at the direction the CBI investigations would take, and could ask Bansal to quit or ease him out in a minor cabinet reshuffle.
Congress leaders also sought to make a distinction between the cases of Bansal and Kumar.
They said while Kumar may have committed an act of impropriety by vetting an affidavit in the coal blocks allocation case, Bansal's case appeared more serious.
They said there was a possibility that Kumar's portfolio could be changed but added that the next hearing in the coal blocks allocation case was not until July.
They said there was a perception in the Congress that steps were needed to be taken to sustain the momentum of the party's election victory in Karnataka; and media reports of the involvement of two ministers in corruption were not helping matters.
Officially, however, the party has defended its ministers.
Congress general secretary Digvijay Singh said in Bhopal Thursday that no charges had been levelled against Bansal. He added that if the CBI has proof that Bansal was involved in the matter, the party would not spare him.
Singh also defended Kumar, saying that the Supreme Court had not given a verdict, but only made observations on the CBI report on coal blocks allocation.
The apex court had said Wednesday that the heart of the Central Bureau of Investigation (CBI) report was changed on the suggestions of the minister and government officials.
The court had also asked the government whether it was contemplating a law to make the working of the CBI independent, so it could be insulated from extraneous intrusion and interference.
The court's observations came on CBI director Ranjit Sinha's second affidavit, filed Monday, stating that Kumar and senior officials of the Prime Minister's Office and the coal ministry had made certain changes in the probe report on the allocation of coal blocks.
The main opposition BJP has been pressing for the resignation of Kumar and Bansal.