The PM said he received Trivedi's email and formal letter of resignation last night.
He added the new railway minister would be sworn in shortly.
Dinesh Trivedi's resignation is under consideration of Prime Minister Manmohan Singh, finance minister Pranab Mukherjee told the Lok Sabha earlier on Monday.
Responding to a brief impromptu discussion on the issue, Mukherjee, who is the Leader of the House, said Trivedi has sent his resignation to the Prime Minister last evening and it was being considered.
"The Prime Minister has received last night the resignation letter from Dinesh Trivedi. It is under consideration of the Prime Minister," he said.
He also said as per the procedure the letter has to be forwarded to the President, who then takes a decision as per the advice of the Prime Minister.
"As soon as a decision will be taken, the House will be informed of it," he said.
To Opposition leaders' claims that the House had been kept in the dark, Mukherjee said on Friday the Prime Minister had received a communication from Trinamool Congress chairperson Mamata Banerjee and Trivedi had not resigned then.
Mukherjee pointed out that after the presentation of the Union Budget, the Lok Sabha was adjourned till today. He said the government has informed the House of the developments at the earliest opportunity available.
Earlier, Speaker Meira Kumar disallowed notices given by Yashwant Sinha (BJP), Basudeb Acharia (CPI-M) and Gurudas Dasgupta (CPI) for suspension of Question Hour to discuss the issue.
Dasgupta had given a notice for suspension of Question Hour, but the Speaker pointed out that it can be allowed only when there was a Motion being discussed in the House. She, however, allowed the three members to make brief submissions.
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