"They will regret the decision to part ways with us and ask themselves as to why they had done so," Jaitley told BJP workers at a state-level function here without, however, identifying any party.
The event had been organised as part of the drive to collect iron and related material for construction of a statue of independent India's first Home Minister, Sardar Vallabhbhai Patel, in Gujarat. The statue is the brainchild of Gujarat Chief Minister Narendra Modi.
"We did not walk away from our alliance [with JD(U)], but the decision (leading to the ending of the partnership) will nonetheless benefit us and we will perform impressively in Bihar," Jaitley said.
The senior BJP MLA in Bihar Assembly, Ashwani Chaube, will not have to carry out his threat to resign from the House as BJP will do well in the general elections on 40 seats in Bihar, Jaitey added.
Jaitley sought to downplay the threat to BJP from Congress or a likely Third Front configuration, saying that Congress does not inspire confidence among the people while the Third Front was a "losers' front".
"The general elections will prove whether Congress has more votes or hoardings," he said.
As to the Third Front, the senior BJP leader has said earlier that JD(U) would be "squeezed out" in Bihar while Samajwadi Party faced a similar position in Uttar Pradesh.
The designs for the creation of a Third Front would not succeed, he said, adding that the "Third Front is a failed idea".
He was referring to JD(U) leader Nitish Kumar's bid to cobble together a formation of 11 regional and Left parties as an alternative to BJP and Congress-led alliances at the national level.
Any experiment with a Third Front would not be in the national interest and could instead prove to be detrimental to the economy and security of the country, Jaitley said.
He claimed that the people were keen to elect the BJP-led NDA at the Centre under the leadership of Modi.
Exuding confidence about his party's prospects in the upcoming general elections, he said that the outcome of the exercise would be unprecedented and beyond the expectations of all.
The 2014 general elections will turn out to be BJP's best-ever performance and the worst in Congress's history, Jaitley added.
Jaitley also showered praises on Sardar Patel and hailed him for his steely resolve even as he took potshots at the country's first prime minister, Pandit Jawaharlal Nehru, for having 'mishandled' the Kashmir issue.
In contrast to Patel's steadfast efforts at unifying the country, Nehru mishandled the Kashmir issue, he alleged.
Unlike Patel, Nehru's success as a barrister has been glorified even though he was a non-practising advocate all his life, Jaitley further charged.
Lashing out at Congress for stating that Modi had hijacked the legacy of Sardar Patel, Jaitley said that the Gujarat chief minister was only trying to pay tribute to the country's first home minister.
Prominent BJP leaders like Ravishankar Prasad, Rajiv Pratap Rudy, Dharmendra Pradhan and Sushil Kumar Modi, too, spoke on the occasion.
Meanwhile, 10,008 kits containing iron and other material collected from the people of Bihar will be taken to Gujarat for use in the building of the proposed Sardar Patel statue.