TOKYO, June 6 (Reuters) - Japanese government bond yields sank to multi-week lows on Thursday, as robust demand at a sale of 30-year bonds added to buying momentum from a continued slide in U.S. Treasury yields.

The 30-year yield dropped 7.5 basis points (bps) as of 0504 GMT to 2.1%, its lowest since May 22, putting it on track for its steepest decline since December.

The 10-year JGB yield fell 4 bps to 0.96%, the lowest since May 17.

The finance ministry's sale of 680.5 billion yen ($4.37 billion) of 30-year JGBs saw a measure of demand called the bid-to-cover ratio improve to 3.59 from 3.25 at last month's auction.

Yields were already trending lower before the result, tracking a five-day slide for Treasury yields as soft U.S. economic data fuelled bets for Federal Reserve interest rate cuts.

The 10-year JGB yield was as high as 1.1% on May 30 amid building speculation for a hawkish shift by the Bank of Japan at its two-day policy meeting ending June 14.

BOJ Governor Kazuo Ueda on Thursday reaffirmed his resolve to trim the central bank's JGB purchases in comments to parliament, but added that policymakers would move "cautiously" in raising rates "to avoid making any big mistakes".

Japanese central bankers have adopted a more hawkish tone since early last month as the yen's plunge to a 34-year low to the dollar threatened to upend the BOJ's hoped-for cycle of mild inflation feeding steady wage increases.

The BOJ "now has to think seriously about how its reduction in JGB purchases will affect the exchange rate", said Yasunari Ueno, chief market economist at Mizuho Securities, who sees a 1 trillion yen reduction in monthly bond purchases to about 5 trillion yen as likely in the near term.

"Put bluntly, if the Bank mishandles its next move, and selling pressure on the yen increases as a result, we are likely to hear renewed calls for it to be held accountable."

Benchmark 10-year JGB futures rose 0.3 yen to 144.13 yen.

The 20-year JGB yield dropped 6.5 bps to 1.77%.

The two-year yield fell 2 bps to 0.33%, and the five-year yield lost 3 bps to 0.535%. ($1 = 155.8000 yen) (Reporting by Kevin Buckland; Editing by Mrigank Dhaniwala)