(Updates to close) Sept 28 (Reuters) - Australian shares closed...

(Updates to close)

Sept 28 (Reuters) - Australian shares closed on a slightly firmer note on Thursday, tracking strength in U.S. stocks on hopes President Donald Trump's administration may be making progress on a broad U.S. tax-reduction plan.

The S&P/ASX 200 index (xjo) rose 0.11 percent, or 6.117 points, to end at 5,670.4. The benchmark lost 0.1 percent on Wednesday.

Trump proposed the biggest U.S. tax overhaul in three decades, calling for tax cuts for most Americans, but prompting criticism that the plan favours business and the rich and could add trillions of dollars to the deficit.

Financial stocks climbed 0.4 percent, with the "Big Four" banks adding between 0.2 percent and 0.6 percent.

Utilities also boosted the index, with AGL Energy (AGL) edging up 1.7 percent.

New Zealand's benchmark S&P/NZX 50 index (nz50) narrowly snapped four straight sessions of gains, inched down 0.002 percent, or 0.16 points, to 7,913.62.

The country's central bank on Thursday kept interest rates at record lows of 1.75 percent, and hinted at a lower growth outlook due to headwinds in the construction sector, against the backdrop of political uncertainty from an inconclusive national election.

Earlier gains in consumer staples and information technology stocks were offset by losses in energy, utility and healthcare sectors.

The biggest loser on the index was Z Energy Ltd (ZEL), slipping 3 percent, followed by Meridian Energy Ltd (MEL) which hit its lowest in nearly two weeks, down as much as 3.8 percent.