* Aussie index posts lowest close since May 8

* A2 Milk biggest drag in NZ index (Updates to close)

May 15 (Reuters) – Australian shares ended lower on Tuesday, led by losses for National Australia Bank and the nation’s biggest telco operator Telstra.

The S&P/ASX 200 index fell 0.6 percent, or 37.5 points, to 6,097.8, its lowest finish in a week.

NAB slipped to its lowest close since Nov 2016, down 3.4 percent as it traded ex-dividend, while Westpac Banking ended marginally lower. ANZ and Commonwealth Bank rose 0.4 percent and 0.2 percent.

Telstra extended losses and finished the session near seven-year lows, down 5.6 percent.

The company issued a profit warning on Monday and said it expect conditions to remain challenging in 2019 with increased competition stemming from the National Broadband Network roll-out.

Miners BHP and Rio Tinto reversed course during the day and ended lower, in line with the downturn in copper, aluminium and oil prices.

Automotive Holdings Group was the worst performer on the index, down 8.8 percent to its lowest since June last year.

The company said below-expected margin gains in the second half from its franchised dealerships and used car businesses will hit profits.

New Zealand’s benchmark S&P/NZX 50 index closed marginally lower by 4.45 points to 8,708.78, snapping nine straight days of gains after hitting all-time highs in multiple sessions.

Dairy company A2 Milk and Fisher & Paykel Healthcare were the biggest drags, down over 1.5 percent each.