Parker said he did not know why Canada withdrew from the agreement, or whether its withdrawal was short-term or permanent.
He said its disagreement with Vietnam over labour provisions was not the deal-breaker.
"That issue was resolved with a transitional period for them. It would have been resolved by the time of final signature of the agreement," he said.
He also thought it was unlikely that Canada had succumbed to pressure from United States President Donald Trump, who pulled out of the agreement soon after he took office in January.
He said Labour had expressed concerns about five aspects of the agreement before the election. It wanted the ability to stop foreigners buying NZ houses, protection from investor-state dispute resolution, protection of Pharmac's single-buying model for medicines, protection of the Treaty of Waitangi, and "decent tariff reductions into the likes of Japan".
He said all of those issues were resolved to the extent that New Zealand was willing to sign the deal.
The Government had found that it could ban foreign purchases of existing houses before the TPP came into force.
On investor-state disputes, he said: "We had a carve-out of Australian investment into New Zealand from those investor-state dispute resolution clauses, so 80 per cent of foreign direct investment from TPP countries would not have been covered by the investor-state dispute resolution clauses."
He said the previous National Government negotiated protection for the Pharmac model, and added: "We made further improvements in respect of some of the patent provisions."
National had also negotiated protection of the Treaty of Waitangi, and the deal included tariff reductions by Japan.
Parker said there was now no chance of the deal being concluded at the Vietnam meeting, but he said officials would meet again in coming weeks to see whether an agreement could be revived.