BJD leader Bhartruhari Mahtab walked out because the discussion would not benefit Odisha.
The Biju Janata Dal (BJD) members walked out of the Lok Sabha on Friday as the House began a debate on a no-confidence motion moved by the opposition against Prime Minister Narendra Modi's government.
Speaker Sumitra Mahajan said the discussion on the no trust motion would continue for the entire day and the vote would take place at 6 pm.
She said the House would also skip lunch.
Congress leader Mallikarjun Kharge sought more time from the Speaker saying 38 minutes allotted for his party leaders to address the Lok Sabha was not enough.
He also sought more time for the members of Trinamool Congress, Left parties and the Rashtriya Janata Dal (RJD).
"This is a very important motion. The country is watching us to know what we have to say and how the government is going to respond. Don''t limit the time. There are precedents when no-confidence motions have been debated for two, three or even five days. Therefore if you sum up in five hours, it is not justified," Mr Kharge said.
Parliamentary Affairs Minister Ananth Kumar responded, saying Mr Kharge is a senior leader but needed to understand that "in one-day cricket era, there was no need to play a test cricket match for five days".
The BJD, which has 19 members in the Lok Sabha after the resignation of Kendrapara MP Baijyant Jay Panda, then walked out.
Its leader Bhartruhari Mahtab said injustice had been done to Odisha in the last 14 years and the BJP government at the Centre has failed to safeguard the interests of the state.
"In the last 14 years, the BJD has witnessed that the United Progressive Alliance (UPA) for 10 years and the National Democratic Alliance (NDA) for four years have done injustice with Odisha. And this discussion is not going to help Odisha. So we are not going to participate," Mr Mahtab said.
The Telugu Desam Party (TDP), an estranged ally of the Bharatiya Janata Party (BJP)-led NDA government, moved the no-confidence motion on Wednesday, which was admitted by Ms Mahajan.
The no-confidence motion has the support of the Congress, Trinamool Congress, Nationalist Congress Party (NCP), Samajwadi Party (SP), and the Communist Party of India-Marxist (CPI-M).
The ruling NDA, however, enjoys a comfortable majority in the House. The BJP which leads the ruling combine has 273 members in the House that has an effective strength of 533, excluding the Speaker.