"It is important that we give the new President a chance put his team in place and consider his trade agenda. This will obviously take some time. We will be able to work with America on trade.
Now, more than ever, we need to be championing the cause of openness and inclusiveness."
Trump's election has effectively put paid to any hope US President Barack Obama will get it through during his 'lame duck' period.
Prime Minister John Key has conceded there was little chance the TPP agreement would get through in the US in the near future but had not given up all hope, saying Trump would get briefed on its benefits for the US to maintain economic leadership in the Asia Pacific.
The decision to proceed was mocked by Labour, Green and NZ First MPs who oppose the bill.
Trade spokesman David Clark said McClay was the "Patron Saint of Lost Causes."
"He made an earnest plea to this House to support a bill that will not be ratified, that will not enter into force. It is a bill which his own Prime Minister has pretty much said is dead in the water."
Green MP Gareth Hughes said passing the bill was "the definition of futility."
However, McClay defended the decision to continue with the legislation.
"At times when there is uncertainty in the rest of the world, New Zealand's consistent and trusted voice of negotiating trade outcomes that are good for our economy and good for the world's economy, needs to be heard.
Our role is as a champion for trade liberalisation. In this role today this Parliament must show leadership."
Labour, the Green Party, the Maori Party and NZ First oppose the TPP but the legislation has support from National, Act leader David Seymour and United Future leader Peter Dunne.
The trade agreement between 12 Pacific Rim countries took years to negotiate and the New Zealand Government had hoped it would deliver the long sought-after trade agreement with the United States.
Labour has opposed it partly because it prevents a ban on foreign buyers of New Zealand property.
The countries in the agreement are New Zealand, Australia, Brunei Darussalam, Canada, Chile, Japan, Malaysia, Mexico, Peru, Singapore, the United States and Viet Nam.