New Zealand shares rose on Tuesday after a tech rally on Wall Street saw two of the major US indexes start the week with gains.

The S&P/NZX 50 Index gained 0.4% or 49.66 points to close at 13,605.96.

The S&P 500 closed 0.2% higher, and the Nasdaq Composite gained 0.5% on Monday after a deal between OpenAI and Amazon.

OpenAI has entered a seven-year, $38 billion agreement with Amazon.com to purchase cloud services, its first major move to strengthen its AI capabilities following last week's restructuring, which granted the ChatGPT maker greater operational and financial independence, Reuters reported Monday.

In domestic news, Barfoot & Thompson's home sales in Auckland reached 930 properties in October, or roughly NZ$1 billion, down 9.9% from 1,032 homes last month, the real estate agency reported.

In corporate news, Smartpay Holdings (ASX:SMP, NZE:SPY) has completed its scheme of arrangement with Shift4 Holdings, resulting in Shift4 acquiring all the company shares.

Chorus (ASX:CNU, NZE:CNU) issued 374,198 new CIP1 warrants, representing 3.78% of the total, to National Infrastructure Funding and Financing (NIFF), formerly Crown Infrastructure Partners (CIP).