Rising U.S. Treasury yields make dollar investments more attractive, and the case for lifting U.S. rates further was bolstered by Federal Reserve Governor Jerome Powell saying the U.S. economy could be ready for two interest rate increases this year, in September and December.
"My general sense is that if people are looking past Greece, we can return to the (monetary policy) divergence theme ... and when you do that you look at fundamentals. Despite the weak durable goods number this morning, generally speaking I think people see the U.S. economy accelerating, leading to a Fed rate hike," said Marc Chandler, global head of currency strategy at Brown Brothers Harriman in New York.
Euro zone leaders agreed late on Monday that the institutions representing Greece's creditors should try to wrap up a detailed agreement by Wednesday evening for their finance ministers to approve and present to them on Thursday.
That leaves barely 48 hours to scrutinize the complex plan, make sure the numbers add up, agree on a list of "prior actions" to turn the promises into laws quickly, find a legal way of extending the Greek bailout and get Athens the money it needs to pay the International Monetary Fund 1.6 billion euros ($1.8 billion) next week.
Read MoreEurope shares close higher; Greece talks in focus