Oct 3 (Reuters) - London zinc prices fell on Tuesday as a firm dollar made greenback-priced metals expensive to holders of other currencies, while an expected supply increase is likely to weigh on further price rallies.

Three-month zinc on the London Metal Exchange dropped 1.8% to $2,554 a ton at 0453 GMT, retreating from its highest since May 10 of $2,675 a ton hit in the previous session. The contract surged 11% in the third quarter.

Combined zinc inventories in LME and SHFE warehouses eased in the second and third quarters, but still rose 165% year-to-date to 134,904 tons, exchange data showed.

The weekly declining rate has been slowing in recent weeks, according to the data.

The dollar held on to fresh highs on views that the Federal Reserve will keep interest rates higher for longer.

"We expect prices to remain relatively stable over the coming months, as gradually improving mined and refined output helps to reduce market tightness... There are tentative signs that European smelters could begin increasing production again in 2023," Fitch Solutions analysis unit BMI said in a report.

"We maintain our forecast for prices to average $2,550 a ton over 2023, which implies prices averaging $2,212 a ton over September-December. Looking beyond 2023, our longer-term view on zinc prices remains negative," the report said.

LME copper shed as much as 0.6% to $8,004.50 per metric ton, the lowest since May 26, while lead hit a five-month low of $2,137 a ton.

Copper inventories in LME-registered warehouses rose to 169,300 tons, the highest since May 2022. LME lead stockpiles rose to the highest since June 2021 to 78,325 tons.

Meanwhile, data from the COMEX showed money managers were increasingly bearish on copper, with short positions surging to 77,276 contracts, the highest since March 2020.

LME aluminium declined 0.5% to $2,309 while nickel rose 0.3% to $18,800 a ton and tin climbed 1.7% to $23,900.

For the top stories in metals and other news, click or (Reporting by Mai Nguyen in Hanoi; Editing by Sohini Goswami)