Almost the same number, 25.8 per cent oppose it on the basis of the investor-state dispute settlement provisions, down 5.5 points from the same questions asked in September.
But 45.9 per cent formed no view on it, the same as September.
The TPP was settled among 12 countries: New Zealand, Australia, the United States, Japan, Canada, Mexico, Singapore, Brunei, Malaysia, Vietnam, Chile and Peru.
It won't enter into force until the US and Japan have ratified it.
In New Zealand, the deal will be subject to a national interest analysis by officials and together with the final TPP text, will be scrutinised by the foreign affairs and defence select committee.
Any associated legislation will have to be passed by Parliament.
Once those two steps are completed - the cabinet will commit New Zealand to it - all parties have up to two years to ratify it.
Mr McClay told the Herald that he would not rush the process and envisaged it taking a year to get through, although he wanted New Zealand to be one of the first to ratify it. "I'll be looking to take a good amount of time to do this. It is a 6000-page document," he said.
"I think it is important that all New Zealanders have an opportunity to understand it better and to have their say through the parliamentary process. But at the same time we want to be one of the countries that gets it ratified and in place at the front of the queue."
Mr McClay said the TPP had caused more anxiety than any other trade agreement he could think of and yet it was an "exceptionally high quality" agreement.
"So we will be looking at getting out with some of our experts to talk about TPP more. We'll be doing that through the course of the year."
He said final plans were still being worked on but in his view, ISDS was an important part of the the deal because it protected New Zealand investors in overseas markets.
He said TPP could not be misused - and tobacco companies could not use ISDS at all.
The US joined the talks in 2008 under President Bush just before he left office and it took until 2010 before Barack Obama's Administration signed up to the negotiations.
It then led them for the next five years, bringing Japan into the process in 2013.
The TPP will eliminate tariffs on 93 per cent Zealand exports except two categories: beef into Japan and dairy products into Japan, US, Canada and Mexico.
Beef tariffs into Japan will be reduced. Tariffs on some dairy products will be eliminated or reduced but tariff quotas will be introduced on some dairy products.
The Ministry of Foreign Affairs and Trade estimates TPP will add $2.7 billion a year to New Zealand's GDP by 2030.
Mr McClay has already had early success in his role as Trade Minister; he attended the World Trade Organisation ministerial conference in Nairobi this month at which export subsidies were eliminated by its 163 members.
The poll of 750 eligible voters was conducted by DigiPoll between December 4 and 14. It has a margin of error of plus or minus 3.6 per cent.
