NEW YORK (CNN/Money) - The dollar remained weak Tuesday against the euro as European finance ministers angled away from intervention to make the euro more competitive.

Meanwhile, the falling dollar underscored the concern that overseas investors may begin to pull out of dollar-denominated securities as their value fades.

At around 3:50 p.m. ET, the euro bought $1.2698, up from $1.2686 late Monday while the greenback bought ¥105.53, down from ¥105.61 late in the previous session.

Euro zone finance ministers said after a meeting late Monday that they had not discussed intervening in the foreign exchange market to stem the euro's strength.

Speaking Tuesday, Austrian Finance Minister Karl-Heinz Grasser said the world economic recovery was more important than the euro's rise against the dollar, which would have only a small impact on growth if it continued.

Traders will listen closely to Alan Greenspan's words Wednesday when the Federal Reserve chairman testifies before Congress, and any signs of an impending hike in interest rates could boost the dollar while driving down bond prices.

"The issue is will [Greenspan] have a more hawkish stance than he has (had) before. I think he will because I think that's what the Fed started to do with changing the statement," Adrian Schmidt, senior FX strategist at Royal Bank of Scotland, told Reuters.

Higher interest rates make some U.S. investments, such as CDs, more attractive to overseas investors, thus supporting the dollar. It also indicates the Fed may be seeing signs of inflation, a concern of Treasury investors.

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"If Greenspan signals more of a turning point in the U.S. rate cycle, that could be positive for the dollar, but we don't expect that in the near term," Peter Fontaine, currency strategist at KBC in Brussels, told Reuters.

In the bond market, Treasury prices sagged after staging a short-lived rise following the government's first-quarter debt auction.

The benchmark 10-year note fell 11/32 to 101-6/32 with a yield of 4.10 percent, up from 4.05 late Monday. The 30-year bond lost 18/32 to 106-15/32 with a yield of 4.94 percent, up from 4.92 late Monday.

The two-year note dipped 4/32 to 100-4/32 to yield 1.81 percent, and the five-year note shed 8/32 to 100-20/32 to yield 3.11 percent. Bond prices move inversely to yields.

The Treasury Department said it allotted $24 billion in three-year debt for a high yield of 2.33 percent, while investors applied for more than twice the amount of paper on offer.

The auction, with a bid-to-cover ratio of 2.27, became the most highly-subscribed auction since the three-year note was relaunched last year. Treasury statistics showed indirect bidders, which include overseas central banks, took nearly half the paper.

"It's a fairly robust auction. The 46-odd percent is significantly more robust than average participation rate for last three three-year note auctions. Clearly, this continues to indicate there is fairly good overseas investor participation," said Gemma Wright, debt strategist for Barclays Capital.  

--from staff and wire reports