NEW YORK (CNN/Money) - The dollar hovered near its four-year low against the euro while Treasurys surged on speculation that the Federal Reserve is considering an inter-meeting rate cut.

Bond traders are eagerly awaiting Wednesday's testimony by Federal Reserve Chairman Alan Greenspan on the economy and monetary policy before the Joint Economic Committee of Congress.

Fresh buying was tied to talk that an advisory service told clients the Fed is likely to cut interest rates before the June 24-25 meeting of the central bank's policy-makers -- although such talk has been in the market for several days.

Just before 3:45 p.m. ET, the 30-year note rose 61/32 of a point in price to 116 even, sending its yield down to 4.37 percent from 4.47 percent late Monday afternoon. The benchmark 10-year note also rose 30/32 of a point to 102-3/32, its yield slipping to 3.38 percent, another 45-year low, down from 3.45 percent late afternoon Monday.

The five-year note rose 16/16 of a point to 101-13/32, yielding 2.32 percent, while the two-year note added 5/32 of a point to 100-21/32, yielding 1.28 percent. Yields and prices move in opposite directions.

Policy makers left the fed funds rate unchanged at 1.25 percent at their last meeting, but said the risk in the economy is of more weakness ahead, implying the possibility of a rate cut at the Fed's June meeting, if not sooner.

Concerns about another terrorist attack are also keeping Treasurys well bid. The U.S. embassy and consulates in Saudi Arabia will remain closed on fears of more attacks following last week's suicide bombings, U.S. officials said Tuesday.

The Office of Homeland Security raised the national terror alert level to orange, the fourth-highest rating on five-color scale, Tuesday based on concerns of another possible attack.

"Part of this strength is related to the perceived increased terrorist risk," said Brian Robinson, senior bond strategist at 4Cast Ltd.

Meanwhile, the dollar remained humble after hitting a new four-year low against the euro in early trading Monday and a two-year low against the yen.

The initially sharp drop Monday was a reaction to Treasury Secretary John Snow's comments at a weekend G7 conference in France, suggesting Washington's lack of worry over the weakening dollar.

At around 3:45 p.m. ET, the euro bought $1.1711, up from $1.164 late Monday. The dollar bought ¥116.72, down from ¥117.15 Monday.

When the euro began trading in the currency market on January 5, 1999, it was introduced at $1.1667 and rose as high as $1.19 on that day before settling at $ 1.1830. The single European currency has steadily declined since then and hit a record low of 83 cents in late 2000. In the past year, however, it has risen steadily against the dollar.

The dollar has been weakening against other major currencies in recent weeks, and U.S. officials as well as those in Europe have not appeared concerned with its decline. There have been reports, however, that the Bank of Japan has been buying dollars to slow the yen's climb.

"The main factor is whether or not there will be further signals of covert intervention in dollar/yen and whether or not [Japan] is satisfied at the current level," Paul Mackel, currency strategist at Dresdner Kleinwort Wasserstein in London, told Reuters.  

-- from staff and wire reports