* Aussie PM to announce manufacturing grants worth A$1.3 billion

* Mining sub-index leads gains as iron ore soars

* a2 Milk among top drags on NZ benchmark for 4th day

Oct 1 (Reuters) - Australian shares rose on Thursday, following an upbeat session on Wall Street as talks progressed on a new coronavirus relief package, while easing restrictions in major Australian states also restored confidence in riskier assets.

The S&P/ASX 200 index gained up to 0.9% in early trade and was set to snap a three-day losing streak. The benchmark had closed 2.3% lower in the previous session.

U.S. stocks closed solidly higher on Wednesday, as investors looked past a chaotic U.S. presidential debate at a spate of positive economic data and talks of a coronavirus relief package that could be worth trillions of dollars.

In Australia, the state of Queensland said it would ease restrictions on some people entering from the country's most populous state, New South Wales, while case numbers in the coronavirus hotspot of Victoria remained steady.

Later in the day, Prime Minister Scott Morrison is set to announce grants worth A$1.3 billion ($930.93 million) to manufacturers, in an effort to revive an economy battered by the pandemic.

All major sub-indexes gained, led by mining stocks, which climbed as much as 2% after iron ore futures soared on Wednesday on supply concerns due to a coronavirus outbreak at Australia's Port Hedland.

Heavyweights BHP Group and Rio Tinto climbed as much as 2.6% and 2.1%, respectively.

The tech sub-index jumped up to 1.6%, helped by gains in Afterpay and EML Payments, with both adding more than 3%.

Financials advanced as much as 0.7%, while energy stocks rose up to 0.9%.

In New Zealand, the benchmark S&P/NZX 50 index rose 0.1% to 11,759.5 by 0124 GMT. The top percentage gainer on the index was Oceania Healthcare , up 2.6%, while a2 Milk hit its lowest in more than six months and was one of the top drags on the benchmark for a fourth day. (Reporting by Arundhati Dutta in Bengaluru; editing by Uttaresh.V)