Sticking to its demand for Swaraj's resignation and a high-level probe, the Left party also objected to the Minister making a statement in "the absence of entire opposition" in Lok Sabha.
CPI(M) General Secretary Sitaram Yechury said the Union Minister will be welcomed "with honour" if a probe proves her innocence.
The Left party also demanded resignation of Rajasthan Chief Minister Vasundhara Raje over her alleged help to the controversial former IPL chief Lalit Modi and that of Madhya Pradesh Chief Minister Shivraj Singh Chouhan in connection with the Vyapam scam.
"The Minister gave a statement in the absence of entire opposition like Mr Rajiv Gandhi had run Parliament during the Bofors scam. If at all what the Minister has said is correct, then why is the Prime Minister hesitating to order an inquiry?" Yechury asked.
He stressed that the opposition is demanding only a high-level probe and that the leaders allegedly involved in the controversies should step down till probe is completed.
"If what the Union Minister is saying is correct, then she should come back with honour. (But) let the inquiry prove it," he added.
She insisted she had made "no request or recommendation" to UK government for giving travel documents to Lalit Modi but had left the decision to Britain.
Swaraj, whose ouster is being demanded vigorously by the opposition leading to a deadlock in Parliament, made a statement with a preface in which she regretted that "her friends" in the opposition had been targeting her and were not even ready to listen to her version on the issue.
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