"The general theme is obviously more optimistic that Greece will be able to get a near-term deal," said Edward Acton, Treasury strategist at RBS Securities in Stamford, Connecticut.
The selling pressure began overnight. Treasurys prices pared losses at the start of the U.S. trading session, which analysts attributed to the absence of an announced deal, but quickly retraced losses after better-than-expected U.S. existing home sales data for May supported expectations that the Fed would begin hiking interest rates in September.
Read MoreKey actors to take stake in Greek drama in the week ahead
The National Association of Realtors said on Monday existing home sales increased 5.1 percent to an annual rate of 5.35 million units, the highest in five and a half years. The data was the latest indication that housing and overall economic activity were gathering steam in the second quarter.
"This is just another good, solid report that tells you that the Fed has the ability to go in September if they choose to," said Sean Murphy, a Treasurys trader at Societe Generale in New York.
Traders also awaited this week's $90 billion in new Treasury note supply, which analysts said may have exerted additional pressure on U.S. Treasury prices. Traders typically sell Treasurys ahead of auctions to make room for new supply.
Read MoreFed won't hike rates because they're too scared: Economist
U.S. 30-year Treasurys were last yielding 3.15 percent, compared to 3.06 percent late last Friday. Benchmark 10-year yields were at 2.36 percent, from a yield of 2.27 percent late Friday.
U.S. three-year note yields were at 1.03 percent, from a yield of 1 percent late Friday.