Mr Jones had enjoyed a "free rein" from party leadership this year, Mr Cunliffe said.
"He's had my full support on the great work that he's done on the supermarkets issue and other issues."
Mr Cunliffe said he didn't know if the National party had attempted to court any other Labour MPs and he was sure there would be a place in the Labour Party caucus for Mr Jones if he changed his mind.
Mr Jones told the Herald last night he would leave Parliament next month after he was shoulder tapped by Foreign Minister Murray McCully for a new role as a roving economic ambassador across the Pacific.
He said his unsuccessful bid to become leader last year was part of his decision, but he also wanted to try a new opportunity.
"Over Easter I just had a deeply introspective time and was truthful to myself. I don't want to do it any more. The leadership had a bit to do with it, but I'm 55 this year and I just want to go and do something else. I'm not able to give to Labour the 100 per cent that I ought to be giving. They need a team to stay for the long term and I'm not in that space."
Mr Jones said he had worked hard to expose Countdown's alleged mistreatment of New Zealand suppliers. His campaign forced a Commerce Commission investigation into the issue.
The decision had "absolutely nothing to do with party unity", Mr Cunliffe said.
On TVNZ's Breakfast show this morning Mr Jones said he would not be returning to the political sector. "I've made my decision and I'm moving on."
"The political collar has chafed this dog's neck and now I've slipped the collar."
Mr Jones' resignation opens a position for Kelvin Davis, Labour's candidate in Te Tai Tokerau.
Mr McCully confirmed he had shoulder-tapped Mr Jones this year to ask him to consider taking a new role working on New Zealand's economic development aid programme across the Pacific and in other small developing countries.
He said his experience on the Maori Fisheries Commission and commercial background fitted the role perfectly. He said Mr Jones would also play a role in New Zealand's bid for the Security Council and the Small Island Developing Nations meeting in Samoa this year.
Mr Jones denied being a "sellout" in leaving for a role offered by the National party.
"Being in politics is also like being at a holiday inn, you serve your time and then the next person arrives to take your place," he told RNZ this morning.
New Zealand First leader Winston Peters told RNZ Mr Jones' departure would be a "loss to Parliament, it'll be a major blow to the Labour Party and an even bigger blow to Maoridom".