The announcement on Monday by the Democrat, Chart Thai and Mahachon parties, came after Thaksin agreed to hold talks with them, but not to accept their proposals.
The opposition plan was not publicly announced but reportedly called for Thaksin to step down from office until the elections are held.
Thaksin said the election would go ahead regardless of any boycott.
The moves by both sides intensified a political crisis triggered by a growing mass movement demanding that Thaksin should step down because of alleged corruption and abuse of power.
In an effort to head off the growing campaign against him, Thaksin dissolved Parliament on Friday, forcing national elections three years earlier.
His party is widely expected to win because of its massive financial resources and control over government.
Sukhum Nuansakul, a political lecturer at Ramkhamhaeng University, said:"Once the opposition parties decide that they will not join the election, many more problems will arise for the government, and there might not even be an election on 2 April."
The opposition wants Thaksin to
resign before the April elections
Abhisit Vejjajiva, the Democrat party leader, along with the leaders of the two other parties at his side, said the lack of a positive response from Thaksin to their reform proposals "means the government is not sincere about political reforms".
The parties also decided not to attend a planned meeting with Thaksin later on Monday after he publicly rejected their proposals in advance.
Abhisit blamed Thaksin for the worsening situation. He said: "The government actions will lead to a further political crisis, so the three parties have decided to not join the meeting with the prime minister and will not join the elections."
Thaksin, responding to their decision, said his Thai Rak Thai Party "has done its best".
He told reporters: "What the opposition parties do is up to them."
On Sunday, tens of thousands of protesters demanded Thaksin's resignation during a rally at a large field near the old royal palace in Bangkok, where thousands camped out overnight, and many said they planned to regroup later on Monday.
Many of Thaksin's opponents believe that constitutional reforms are needed to loosen the ruling party's stranglehold on power.
"What the opposition parties do is up to them"
Thai Prime Minister
Thaksin, while willing to consult with the opposition, said he would not sign a plan they planned to submit to him, instead offering a longer-term constitutional reform plan.
Thaksin, one of the country's richest men, won a second term as prime minister a year ago with a landslide election victory for his party, which won 377 of the 500 seats in the House of Representatives.
In addition to allegations of corruption, he has also come under fire for mishandling a Muslim insurgency in southern Thailand, stifling the press and allowing business and political cronies to reap enormous gains from state policies.