NEW YORK (CNN/Money) - Treasurys edged higher in late Tuesday afternoon trading while the dollar worked to sustain a recovery versus the euro, after hitting new lows against the European currency last week.

A drop in two-year note yields to below the Federal Reserve's 1.25 percent official funds rate shows that the market believes the Fed is willing to cut interest rates again -- by as much as a half-percentage point -- at its June policy meeting.

At around 3:45 p.m. ET, the 10-year note added 20/32 of a point in price to 102-13/32, pushing the yield down to 3.34 percent versus 3.42 late afternoon Monday. The 30-year bond rose one point in price to 116-3/32, pushing the yield to 4.37 percent, down from 4.43 late Monday afternoon.

The two-year note rose 6/32 of a point in price to 100-3/32, with the yield at 1.21 percent, while the five-year note rose 13/32 of a point in price to trade at 101-26/32, with the yield at 2.24 percent.

"This relatively sharp drop in two-year note yields is basically discounting an increasing potential for the funds rate being lowered to 75 basis points," said William Sullivan, economist and executive director at Morgan Stanley.

Participating via satellite on a central bankers' panel with the International Monetary Conference in Berlin, Federal Reserve Chairman Alan Greenspan noted that while deflation was unlikely, taking insurance against it would not cost much.

The dollar continued to recover versus the euro on the back of encouraging comments out of the Group of 8 meeting in Evian, France. French President Jacques Chirac, who hosted the event, said the G8 nations are closely monitoring currency movements and that foreign exchange stability is essential for growth.

President Bush made comments at the G8 meeting during the weekend that seemed to show support for a strong dollar, but he also noted that foreign exchange markets should determine its value.

"The market is now wary of pushing the dollar down too rapidly because of G8 comments. The market is also alert to firmer economic data because it can be potentially supportive of the dollar," Steven Pearson, chief currency strategist at Halifax Bank of Scotland Treasury Services, told Reuters.

At around 3:45 p.m. ET, the euro bought $1.1742, down from $1.1757 late Monday afternoon. The dollar bought ¥119.17, up from ¥118.61 late afternoon Monday.  

-- Reuters contributed to this report.