Gandhi, while congratulating the victorious candidates, said that the results showed the "electorate is very angry with the BJP and will vote for the non-BJP candidate most likely to win".
Tejashwi Yadav said the Samajwadi Party and the BSP should fight the 2019 Lok Sabha polls together and urged the Congress to join them.
"A Grand Alliance is the demand of time, it is the demand of the people. Keep your ego away. There is a need to teach a lesson to those who have destroyed the country," he said.
Sharad Yadav said even "a partial unity" among opposition parties was enough to defeat the BJP.
"The (BJP-led) government will go even if there is a partial unity among the opposition parties," he said.
Asked if the Opposition parties were chalking out unity plans ahead of the 2019 General Election, he said the "process is on" and added that the opposition unity was a "big challenge" and would take "time and honest efforts" to materialise.
Banerjee congratulated Akhilesh Yadav, BSP chief Mayawati and Lalu Prasad as the Opposition took big leads over the BJP in Lok Sabha by-elections.
Uttar Pradesh Chief Minister Yogi Adityanath said that the BJP under-estimated the SP-BSP alliance that led to its defeat in the by-elections to the prestigious Gorakhpur and Phulpur Lok Sabha seats and termed it as a lesson to the party which would do an introspection.
Reacting to the shocking defeat of the party in the seats held by him and his Deputy Keshav Prasad Maurya, he, however, expressed confidence that this would have no impact on the general elections in 2019 in which national issues will play a dominant role and it will be a vote on the performance of Prime Minister Narendra Modi.
He said local factors play a role in by-elections but in the general elections, the good performance of the Modi government and its welfare schemes will have an impact in BJP's favour.
In Bihar, BJP leader and Deputy Chief Minister Sushil Kumar Modi downplayed the RJD's victory, saying it was the result of sympathy votes in Lalu Prasad's favour.
(With Agency inputs)