Peters said he's had conversations with US Vice-President Mike Pence about this very matter, who assured him work was being done to progress the deal.
He said he was working "very seriously" on securing the lucrative trade deal between the two countries.
US goods and services trade with New Zealand totalled an estimated US$13.4 billion in 2017.
Last year, New Zealand was the United States' 48th largest goods export market.
In early 2017, US President Donald Trump pulled the US out of the then-called Trans-Pacific Partnership (TPP).
The US being in the agreement with New Zealand would have essentially meant the two countries had a free trade agreement.
However, after pulling out of the deal, Trump instructed officials to "begin pursuing, wherever possible, bilateral trade negotiations to promote American industry, protect American workers, and raise American wages".
He indicated that it was better for the US' interests if it had one-on-one trade deals, rather than a deal with multiple different countries.
Since then, New Zealand has been pursuing a one-on-one bilateral trade deal with the US.
Meanwhile, the trade war between the US and China has again heated up.
This week, the US more than doubled the tariffs – tax on imported products – on US$200 billion of Chinese imports.
China hit back, saying it would impose tariffs on US$60b of US goods from June 1.
Peters told RNZ the escalating trade war was concerning for New Zealand as "there will be a knock-on effect and it could very likely affect New Zealand adversely".
