* Mining stocks hit their highest since May 2011

* Fortescue Metals hits all-time high

* James Hardie Industries top performer on the benchmark

* NZ dips as healthcare and consumer stocks drag

Aug 11 (Reuters) - Australian shares rose to a three-week high on Tuesday, boosted by heavyweight financial stocks, after the country's second-most populous state reported a small rise in new COVID-19 infections, lifting investor sentiment.

As of 0106 GMT, the S&P/ASX 200 index rose 0.56% to its highest since July 22. The benchmark closed 1.76% firmer on Monday.

Daily infections in Victoria peaked at 725 on Aug. 5 and have been trending lower in recent days, following the imposition of a hard lockdown in Melbourne on July 19

Investors also eyed stalled U.S. policymakers' efforts to hammer out a coronavirus relief bill.

U.S. congressional leaders and Trump administration officials said on Monday they were ready to resume negotiations on a coronavirus aid deal, but talks remained deadlocked.

Back home, solid gains in Australian banks helped the financial sub-index rise 1.2% to its highest since July 30.

The country's largest lender, Commonwealth Bank of Australia , which is slated to report is annual results on Wednesday climbed 1.7%, while the rest of its "Big Four" peers added between 2% and 2.3%.

Mining stocks climbed 0.8% with the world's fourth-largest iron ore miner, Fortescue Metals Group, adding nearly 2% to hit a record high after it won a tender to supply Chinese steelmaker HBIS Group.

James Hardie Industries, the world's biggest fibre cement maker, jumped 6% to a six-month high, making it the top performer in the local benchmark index as the company forecast higher full-year earnings from an improving U.S. housing market.

However, gold stocks fell about 1.2% as bullion prices retreated from an all-time high hit in the previous session.

Losses in the sub index were led by De Grey Mining , down 4.8%, followed by Alacer Gold Corp, which fell 4%.

In New Zealand, the benchmark S&P/NZX 50 index dipped 0.2% at 11663.72 points by 0111 GMT.

The country's largest construction firm Fletcher Building lost as much as 3.4% after it forecast its first annual net loss in two years and warned of persistent challenges across its supply chains in the year ahead. (Reporting by Deepali Saxena, Editing by Sherry Jacob-Phillips)