"We're not promising a new tax. The only thing that is being considered is whether we should extend the period for the brightline test," he said.
Parker then said the brightline test was not a capital gains tax, it was an "income tax".
But these comments appear to be at odds with comments by Finance Minister Grant Robertson before the election.
Speaking at the launch of Labour's tax policy in September, Robertson was clear about his party's plans on any further tax.
"Labour will not implement any new taxes, or make any further increase to income tax next term."
National has taken issue with this, given Parker this morning described the brightline test as an income tax.
The party's Shadow Treasurer, Andrew Bayly, said Parker's comments show Labour is already wobbling on its election promise not to alter income taxes this term.
A spokesperson for Parker said extending the brightline test was not a new tax: "National is getting ahead of itself because no decision has been made."
Earlier this week, Robertson revealed he had asked the Treasury for advice on extending the brightline test.
At the moment, the brightline test means if someone sells a non-family home within five years they have to pay tax on it.
Bayly said extending the test wouldn't do anything to address the issue of house prices.
Act leader David Seymour made the same argument and said it was a "capital gains tax by stealth".
Despite National and Act's objection to the extension, both parties voted for the bill when it was introduced by the then National Government in 2015.