Mr Jones said he was humbled by the poll result. It showed he had picked himself up off the canvas and it was now up to his caucus members.
"I know Dave Cunliffe has got a host of supporters," Mr Jones told the Weekend Herald. "But Grant's supporters have really got to ask themselves 'what's the point?"'
The result reflected what he was hearing on the street, Mr Jones said. He had wanted to make himself the people's champion. He said he had MPs from both the Cunliffe and Robertson camps contacting him to say they were jumping camps to support him and he wanted more.
"I am just encouraging my caucus colleagues to back me."
He was aware both his rivals appealed to "swathes" of core Labour membership "but I'm interested in having a party that now appeals to New Zealand people".
"I accept I've got limited support in our caucus but I would say to the ABC club (Anyone But Cunliffe), time to go back to one, two, three of politics. Do you want someone who can broaden, deepen and develop the appeal of the party to people beyond the beltway?"
He said he spoke without notes and was trying to show to Labour meetings that in order to match Prime Minister John Key "you've to be able to give a speech, electrifying a crowd, engage the public with no cue cards, no prompts, no speech notes".
Mr Key had an amazing ability to connect and communicate with Kiwis which should not be underestimated.
Mr Jones gained momentum on the hustings this week but he is still considered the more likely of the three to drop off first in the preferential voting system because his support in the caucus is limited.
The caucus votes will comprise 40 per cent of the final result, the membership 40 per cent and the affiliated unions 20 per cent. The leader will be announced on September 15.
Mr Robertson is understood to have a majority of the caucus behind him. Commenting on last night's poll, he said that in many ways it was about name recognition. "And both David and Shane have been in the public eye for a longer period than I have."
He was not worried by the poll and was focusing on the people who would actually vote. "I am getting a good reaction from them as I go around the country and I'm still feeling optimistic.
"I think from here on we are moving into territory where I will do well - here in Wellington, down in Dunedin, and Christchurch."
Mr Cunliffe said he was campaigning solidly and working for every vote he could get. He said he was energised by the race.
"In politics you often get your energy by the people you are with and I sure am."
None of the three candidates said he was advising people on how to rank their preferences beyond their first one.
The 3 News poll of 500 voters was conducted by Research Now and has a margin of error of 4.4 per cent.
How they rate
General voters
• David Cunliffe - 39.6%
• Shane Jones - 31.6%
• Grant Robertson - 28.8%
Labour supporters
• David Cunliffe - 45.6%
• Shane Jones - 28.1%
• Grant Robertson - 26.4%
Source: 3 News Poll
