Jha will contest against National democratic Alliance's nominee Harivansh of the Janata Dal-United.
President Murmu said the new Parliament building "is an important milestone in our democratic journey".
The deputy chairman said Singh's action was in utter disregard of rules and the authority of the Chair.
Ahead of his Dussehra rally, Maharashtra Chief Minister Eknath Shinde on Wednesday tweeted a couplet by famous Hindi poet Harivansh Rai Bachchan, which said that whosoever is his heir will be his son and not vice versa.
When the House assembled at 3 pm following an adjournment post-lunch, the opposition members again started their protest inside the Well and continued their sloganeering.
Prime Minister Narendra Modi on Monday unveiled the national emblem cast on the roof of the new Parliament building.
Rajya Sabha proceedings were adjourned for the day on Tuesday after repeated stoppages as opposition members continued to protest demanding the revocation of suspension of 12 members.
The protesting MPs did not accept the tea and snacks offered by the deputy chairman.
Derek O'Brien of Trinamool Congress came near the podium and tried to show the rule book to the Deputy Chairman. An attempt was also made to snatch the microphone and the marshals tried to prevent it.
Union Home Minister Amit Shah asked the opposition on Monday to allow a debate on the Manipur issue to begin in Parliament but the deadlock persisted in Lok Sabha and Rajya Sabha as both sides refused to budge from their stand, with Congress and its allies insisting on a statement from Prime Minister Narendra Modi first.
The Rajya Sabha was adjourned twice while the opposition parties staged a walkout in Lok Sabha on Tuesday, voicing their protest against the increase in the prices of petrol, diesel and cooking gas LPG.
Leader of Opposition Mallikarjun Kharge sought to raise the issue of inflation and price rise and demanded a discussion on it. The deputy chairman said it cannot be entertained as the Question Hour was on.
It was after a gap of two decades that saw such an occasion where MPs of the upper house enthralled their fellow colleagues at a dinner hosted by Chairman and Vice President M Venkaiah Naidu for 72 retiring members.
What some of our leaders were up to on Thursday and Thursday.
'Meddling with our national emblem was totally unnecessary and avoidable'
Rajya Sabha proceedings were adjourned for the day as amid uproarious scenes with the opposition and treasury benches shouting slogans.
'There is one negative thing which has happened very quietly. The position of the election commissioner has been downgraded.'
Among the suspended members, six are from the Congress, two each from the TMC and Shiv Sena and one each from the CPM and the CPI.
Parliament's Budget session has been a washout since the beginning of its second part on March 13, with the BJP demanding an apology from Gandhi.
Singh said in a statement in the Lok Sabha that all efforts were being made to save IAF Group Captain Varun Singh, the lone survivor of the crash near Coonoor in Tamil Nadu on Wednesday, who was on life support at the military hospital in Wellington.
Modi said the new Parliament reflected the aspirations and resolve of the "new India" to set and work towards achieving new targets.
The suspended Rajya Sabha parliamentarians, who spent the night on the lawns near Mahatma Gandhi's statue in what several old-timers said was the first such overnight protest in the complex, got a surprise visitor in the morning -- Rajya Sabha Deputy Chairman Harivansh who came with tea and snacks.
Finance Minister Nirmala Sitharaman's Budget speech on Wednesday was marked by the usual thumping of benches by the ruling alliance members, but the loudest cheer was reserved for her announcement of income tax relief, which was welcomed by 'Modi, Modi' chants in Lok Sabha that also witnessed a few instances of protest by the Opposition.
Singh noted that opposition members tore rule book, threw papers at the desk of the Rajya Sabha Deputy Chairman Harivansh, who was in the Chair, and climbed the officials' table -- something, he added, he had never witnessed before.
Replying to the Motion of Thanks to the President's address, Modi in the Rajya Sabha had referred to the manner in which Telangana was formed.
The fight would become more interesting as both candidates hail from Bihar, where the assembly elections are to be held soon, making it effectively a JD-U versus RJD contest.
Ganguly broke down as she raised the issue of eight people, including two children, being burnt to death in Bogtui village in Birbhum, saying to be born in West Bengal is not a crime.
Rajya Sabha proceedings were adjourned for the day on Monday amid protests by Opposition parties over their demand to revoke the suspension of 12 members of the House.
The Left parties hit out at the Bharatiya Janata Party-led Centre on Monday over a religious ceremony performed at an event to unveil a cast of the national emblem on the new Parliament building premises, saying such installations should not be linked to religion.
'I grew up in a place that used to be the best city in India: Allahabad.' 'The city has given some of the best writers, politicians and musicians to the country. 'Today, it has gone to the dogs.'
Lok Sabha proceedings were adjourned for the day on Friday amid protests by opposition and Bharatiya Janata Party members over Congress leader Adhir Ranjan Chowdhury's remark on President Droupadi Murmu.
'We strongly object to raising the internal issue of India here and we also reject the politicisation of this forum'
The Congress will reach out to various parties in this regard.
"The conduct of opposition leaders in the Upper House of Parliament on Sunday was shameful, irresponsible and utter disrespect to parliamentary rules and dignity," Union Minister Ravi Shankar Prasad said.
The parties that have submitted the notice include the Congress, All India Trinamool Congress, Samajwadi Party, Telangana Rashtra Samithi, Communist Party of India, Communist Party of India-Marxist, Nationalist Congress Party, Rashtriya Janata Dal, National Conference, Dravida Munnetra Kazagham and the Aam Aadmi Party.
Opposition leaders and activists have accused the government of distorting the national emblem by replacing the 'graceful and regally confident' Ashokan lions with those having menacing and aggressive posture, and sought immediate change.
The disruption by Opposition members drew sharp criticism from Prime Minister Modi who accused them of being unable to digest the fact that a large number of new ministers are women, Dalits, tribals and those from other backward classes
Rajya Sabha witnessed unruly scenes on Sunday as Opposition members stormed the well and reached the deputy chairman's seat to protest against the farm bills debated and passed by the Upper House through voice vote.
The Rajya Sabha proceeding washed out completely on Wednesday and was adjourned for the day amid continued protest by the Opposition parties led by the Congress over price rise and levy of Goods and Services Tax (GST) on daily essentials.
Bihar Chief Minister Nitish Kumar's Janata Dal-United on Wednesday asserted that it was "not scared of ED and CBI" following its break-up with the Bharatiya Janata Party, which rules the Centre and is often accused by the opposition of misusing investigating agencies.