Balls insisted he did not want to get involved in speculation about post-election deals after appearing to have eight opportunities to rule out a Labour-SNP agreement on the Andrew Marr Show.
Opinion polls suggest the SNP are set to make huge gains north of the border, which could influence the future of a Westminster government.
Speaking on the BBC One programme, Balls said parties who ignore the need to tackle the country's deficit are "completely wrong" and "irresponsible".
He went on: "We have no plans, no need, no desire to have any deal with the SNP. This is a party which wants to break up the United Kingdom. They're not going to be able to stand up for the whole of the UK."
Told by Marr to say the words "I rule it out", Balls replied: "Ed Miliband said it's nonsense. It's not part of our plans.
"You know Andrew, you've been covering politics for 30 years, parties, large parties at this stage say we're fighting for a majority and we are. I'm not going to get involved in speculation about post-election deals. We're fighting for a majority."
Balls said he did not think the speculation over a potential deal was damaging to Labour's election prospects, as he sought to turn attention on to reports on the potential of a Ukip-Tory pact.
Told there must be a reason he could not rule out an SNP pact, Balls replied: "What I will not do at this stage is say anything other than we're fighting for a majority."
He added the Tories were now vulnerable over the issue of deals, adding: "We don't want any deal with the SNP. It's not part of our plans. It's nonsense. It's not something we want."
Marr encouraged Balls to say "and we won't do it".
The Labour MP repeated he would not get involved in speculation while the party is fighting for a majority.
Told the speculation goes on, Balls said: "I think it's the Tories and Ukip who are doing the deal and it's probably happening in (Conservative Chief Whip Michael Gove's) kitchen."
Asked how many kitchens he has, Balls failed to answer - instead suggesting people around the kitchen tables of the country were debating the dangers of the Tories rather than how many "kitchen tables David Cameron has got".
The question emerged after Labour leader Ed Miliband was filmed drinking tea in a modest kitchen but it later emerged that it was "the small one". Miliband was dubbed "Two Kitchens" by political opponents - a reference to former deputy prime minister John Prescott's nickname of "Two Jags".