“The anxiety surrounding the Greek referendum remains at a fairly high pitch,” said Edward Acton, a U.S. government-bond strategist at RBS Securities Inc. in Stamford, Connecticut, one of 22 primary dealers that trade with the Fed. “We may grind lower in yields.”

The Treasury 10-year yield fell 14 basis points, or 0.14 percentage point, to 2.34 percent at 2:18 p.m. New York time, according to Bloomberg Bond Trader data. The yield fell as much as 18 basis points, the most since Oct. 15. The 2.125 percent note due May 2025 climbed 1 5/32, or $11.56 per $1,000 face amount, to 98 1/8.

Fed funds futures show there’s a 30 percent chance the Fed will increase its benchmark rate from near zero in September, down from 38 percent on June 26, and a 67 percent chance by December, down from 73 percent, according to data compiled by Bloomberg.

Eoin Treacy's view

Uncertainty is never welcome in the stock market but bonds tend to attract funds when people have doubts about what else to do with their money. Against a background of zero interest rates, wage growth and agricultural commodity prices that are now rising, there are medium-term risks to owning bonds. However, in the short-term traders are probably concluding that they represent less risk than the impact a potential exit of Greece from the Eurozone could have on stocks. 

Greek 2-year yields doubled over the weekend and in response the 30-year Treasury future was up 3 points for a 20 basis point contraction on the yield. Some consolidation of the recent advance in the yield is now looking more likely than not but a sustained move below the 200-day MA, currently near 2.90%, would be required to question medium-term scope for continued higher to lateral ranging.