New Zealand shares fell on Tuesday as most Asian indexes saw losses amid US President Donald Trump's increasing interference with the country's central bank.

The S&P/NZX 50 Index fell 0.93% or 121.52 points to close at 12,957.98.

President Trump on Tuesday said he was firing Federal Reserve Governor Lisa Cook over alleged improprieties in obtaining mortgage loans, Reuters reported on Tuesday.

"All of this, tariffs included, is just another reason the U.S. can't be trusted. There's no credibility. That's the basis of the U.S. being the safest investment in the world. If you're a responsible investor, it gives you pause," said Bart Wakabayashi, the Tokyo Branch Manager of State Street, as quoted by Reuters.

In domestic news, New Zealand's economy is still on a route towards recovery, even if it is a little delayed, said ANZ in a report.

Also, total new residential mortgage lending in New Zealand rose to NZ$9.04 billion in July from NZ$8.26 billion in June, according to data from the Reserve Bank of New Zealand released Tuesday.

In corporate news, Vulcan Steel (NZE:VSL, ASX:VSL) agreed to acquire Roofing Industries, including its interest in all non-wholly owned branch companies, for NZ$88 million.

Bega Cheese (ASX:BGA) and Fonterra Co-operative Group (NZE:FCG) agreed to resolve the dispute in relation to certain licenses, and that the legal proceedings brought against Bega by Fonterra Brands (Australia) and Bonland Cheese Trading should be discontinued.