* Benchmark set for fifth straight weekly gain

* Miners lose steam, fall up to 0.7%

* NZ's Fonterra narrows 2020/21 farmgate milk price forecast

Dec 4 (Reuters) - Australian shares gained modestly on Friday as financials kept the benchmark afloat, offsetting losses in miners following a record rally in the previous session on the back of rising iron ore prices and a lowered forecast from Brazilian miner Vale.

The S&P/ASX 200 index rose 0.2% to 6,626.0 by 2345 GMT, and was on track for its fifth consecutive weekly gain, likely adding 0.4%.

Financials were the biggest boosts to the index, jumping 0.7%, with all "Big Four" banks trading in the black. Top lender Commonwealth Bank of Australia rose 0.8%, while conglomerate Macquarie Group advanced 2.2%, extending gains from the previous session.

However, financials were set to snap a four-week winning streak, losing about 0.5%.

Top drags on the index, miners fell up to 0.7%, losing momentum after three straight gain sessions on the back of a rally in iron ore prices and a downgraded forecast by Brazil's Vale SA.

BHP Group slipped 0.5% after a nearly 5% jump in the previous session, while Rio Tinto fell up to 0.8% after closing at a 12-year high. Fortescue Metals Group dropped from its record level, losing as much as 0.7%.

The healthcare sector hit its lowest in a month, with ASX-listed Resmed Inc and Fisher & Paykel Healthcare losing up to 1.6% and 2.3%, respectively.

Meanwhile, a media report said Pfizer, with which Australia has a COVID-19 vaccine supply agreement, had decided to slash the 2020 production target for its COVID-19 vaccine owing to supply chain challenges.

Across the Tasman Sea, New Zealand's benchmark S&P/NZX 50 index was trading little changed, after erasing gains of up to 0.5% earlier in the session.

Dairy exporter Fonterra inched higher after it lifted the bottom end of its farmgate milk price for the 2020/21 season on strong demand for its product in China, and across Asia. (Reporting by Sameer Manekar in Bengaluru; Editing by Tom Brown)