* Bonds rally in Asia after Moderna CEO warns on vax efficacy

* Yields set to log monthly declines at most tenors

* Powell testimony to begin at 1500 G

SYDNEY, Nov 30 (Reuters) - Bonds rallied to multi-week highs on Tuesday after the head of drugmaker Moderna raised concerns about the efficacy of vaccines against the Omicron coronavirus variant, and the demand for safe assets seems to have Treasuries set to end the month firmer.

The yield on benchmark 10-year U.S. government bonds fell nearly 5 basis points (bps) to 1.4528% in the Asia session, its lowest since Nov. 9.

Yields fall when prices rise and the rally extends gains made since scientists announced the detection of the Omicron variant late last week. Futures on U.S. interest rates also rallied as traders trimmed rate hike expectations.

Moderna's CEO told the Financial Times https://www.ft.com/content/27def1b9-b9c8-47a5-8e06-72e432e0838f that present vaccines would likely be less effective against the new variant and that it'd be a risk to completely shift production to an Omicron-targeted dose while other variants remain in circulation.

The market moves have 10-year Treasuries heading toward snapping three months of selling to post a monthly gain, with yields down 9 bps as investors reel back wagers on higher rates.

Shorter and longer-dated bonds also rallied on Tuesday.

Two-year yields were down 1.4 bps at 0.4803% at 0737 GMT. Five-year yields were down about 4 bps to 1.1194% and 30-year yields dipped by 2.7 bps to 1.8301%.

"We expect these price movements will extend into the London session," said Commonwealth Bank of Australia strategist Carol Kong.

"In our view, vaccine efficacy will be crucial to the outlook for lockdown restrictions and therefore the global economic outlook."

Ahead on Tuesday, Federal Reserve Chair Jerome Powell and Treasury Secretary Janet Yellen are due to testify before U.S. lawmakers from 1500 GMT.

In prepared remarks already released, Powell noted Omicron posed risks to growth and said inflation could persist longer than first thought. (Reporting by Tom Westbrook; Editing by Kim Coghill)