New Zealand shares fell on Tuesday despite a broader rise in Asian markets after Trump said he will reconsider auto tariffs.

The S&P/NZX 50 Index fell 0.8% or 96.20 points to close at 12,011.34.

Trump said on Monday he was considering a modification to the 25% tariffs imposed on foreign auto and auto parts imports from Mexico, Canada, and other places.

New Zealand's partnership with the United States is among the "most important", especially regarding their joint interests in the Pacific and the evolving security environment, the country's Foreign Minister Winston Peters said.

"We have long advocated for the importance of an active and engaged United States in the Indo-Pacific, and this time in Honolulu allowed us to continue to make that case," he added.

In the local economy, Annual food inflation in New Zealand rose to 3.5% in March from a 2.4% increase in February, Stats NZ said in its selected price indexes report filed on Tuesday.

Additionally, supplier costs for Foodstuffs supermarkets went up slightly in March as Foodstuffs New Zealand Grocery Supplier Cost Index (GSCI), prices from suppliers were 2% higher in March than last year, according to Infometrics.

Also, House values in New Zealand declined in March, while sales increased as cheaper interest rates have pushed more people to buy homes in signs of a "positive shift" in the property market, the Real Estate Institute of New Zealand said in a Tuesday report.

Meanwhile, The Reserve Bank of New Zealand (RBNZ) will launch a depositor compensation scheme on July 1, protecting up to NZ$100,000 per eligible depositor if a licensed bank or financial institution fails, the central bank said on its website.

In corporate news, Auckland International Airport's (NZE:AIA, ASX:AIA) total passenger movements fell 3% year on year to over 1.6 million passengers in March, following a 4% decline in February.

Channel Infrastructure NZ (NZE:CHI) said it is "well positioned" to meet any additional stockholding requirements in line with the government's minimum supply obligation for diesel importers.