* Miners finish lower for third straight session

* Tech stocks end at their lowest in a month

* NZ asks inbound travellers to show negative COVID-19 test

Jan 12 (Reuters) - Australian shares inched lower on Tuesday as concerns over a highly infectious COVID-19 strain weighed on investor sentiment and stoked fears of fresh global lockdowns, though losses were limited by heavy buying in financials.

The S&P/ASX 200 index fell 0.3% to 6,679.1 at the close of trade.

Fears over the spread of a highly infectious UK-linked COVID-19 strain have increased frictions between Australian states regarding restrictions, even as fresh cases in the country remain low.

Western Australia premier Mark McGowan said the country "could rest a lot easier" if the virus was eliminated in New South Wales, which has been fighting to contain low but consistent numbers of community transmissions.

"There is still a lot of potential for things to be further locked down and constricted and the concern over this UK strain of the virus is now being talked about," said Brad Smoling, managing director at Smoling Stockbroking.

There is no effective national plan to control the virus, but rather individual states that make uncoordinated decisions, which creates a wave of uncertainty across the nation, Smoling added.

The metals and mining sub-index was the biggest drag on the benchmark, settling 0.9% lower. Softer iron ore futures due to the present coronavirus situation spurred declines in top miners BHP Group and Rio Tinto.

Local tech stocks ended at a month-low, tracking an overnight rout in U.S.-based peers after tech giants took steps to limit outgoing U.S. President Donald Trump's social media reach.

On the flip side, financials gained 0.7%, with the so-called "Big Four" banks adding between 0.8% and 1.1%.

New Zealand's benchmark S&P/NZX 50 index eased 0.8% to finish the session at 13,183.69.

The country heightened virus screening for inbound international travellers, requiring visitors to show negative COVID-19 test results before boarding flights to the island nation. (Reporting by Arpit Nayak in Bengaluru, Editing by Sherry Jacob-Phillips)