Ten-year Treasuries rose around 4/32 in price to yield 1.618 percent in Asia, down roughly 2 basis points from late US trade on Friday and not far from Friday's trough of 1.599 percent, the 10-year yield's lowest level since Sept. 7.

A drop in equities helped lend support to Treasuries, said a trader for a US brokerage house in Tokyo.

"Whenever we see risk assets in our session trade heavy like it is now, it is tough for us to want to go the other way," he said, adding that trading volumes were low with Chinese markets closed this week for public holidays.

In the stock market, MSCI's index of Asia-Pacific shares excluding Japan fell 0.4 percent.

A near-term focal point for financial markets is a review by Moody's of Spain's sovereign rating.

If Moody's were to downgrade Spain to junk status, that could trigger a rise in bond yields in indebted euro zone countries and give a short-term boost to Treasuries, said a trader for a US brokerage house.

Still, even in that case Spain's borrowing costs will probably eventually come back down, given that Spain has the option of requesting external aid, the trader said.

A formal request for aid by Spain could prompt the European Central Bank to use its new bond-buying programme to help lower Spanish bond yields.