The uproar, unusual on a Budget day, led to the delay in presentation of the document by a few minutes.
As soon as Jaitley rose to speak, Congress and Left members raised the issue of notice of Privilege Motion given by them against Irani over her remarks made in Parliament last week regarding Vemula's suicide.
Despite Speaker Sumitra Mahajan saying that the matter is under her consideration, they kept raising the issue, prompting Parliamentary Affairs Minister M Venkaiah Naidu to accuse them of indulging in "cheap politics" at a time when Budget was being introduced.
Congress member K C Venugopal said "it is painful for me to move Privilege Motion on a day like this."
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Irani was present in the House.
Jaitley started his speech amid the uproar following which opposition members took their seats.
When Jaitley was 20 minutes into his speech, the Speaker said if he so desires, he can sit down and read the remaining text while seated.
She apparently had in mind the health conditions of Jaitley who in 2014 had taken an unprecedented break during his Budget speech due to back pain and had continued reading the document after a 20-minute adjournment of the House.
Around 1130 am, Jaitley today took the permission of the Chair to sit down. When reached the concluding paragraphs of his speech, he stood up to complete the text.
apparently suggest that the previous UPA government had handed over the economy in bad shape and the NDA had corrected the situation.
"Kashti chalane walon nein jab di patwar humein...In haalat mein aata hai dariya paar karna humein (When we were given the row of a ship..We know how to cross the river in these conditions)," the Finance Minister recited.
Later, he said, "'asmani' (celestial) and sultani (empire) powers have troubled us" but did not explain.
As the minister was reading out his budgetary proposals, several of his cabinet colleagues including Manohar Parrikar, Prakash Javadekar and Dharmendra Pradhan were seen jotting down important points.
When Jaitley referred to Dalit entrepreneurs, some Congress members were heard referring to Vemula.
Congress Vice President Rahul Gandhi was seen smiling when the minister mentioned that his suggestion with regard to Braille paper import had been accepted.
Gandhi had urged the Commerce Ministry to slash the import duty on specialised equipment for visually-challenged people after a student from Bengaluru had sought his intervention on the issue.
Members, both from the Treasury and Opposition members were seen smiling and talking to each other but very few thumped their tables to welcome with the hike in excise on tobacco products.
Prime Minister Narendra Modi led the treasury benches in welcoming each proposal announced by the Finance Minister by thumping his table.
When the House was adjourned for the day after presentation of the Budget, Modi was surrounded by leaders of BJP, BJD and other NDA allies. Jaitley too was surrounded by BJP MPs, including several ministers. Some patted his back, while most shook hands with him.