NEW YORK (CNN/Money) - Treasury prices moved sharply higher Tuesday after Federal Reserve Chairman Alan Greenspan said inflation was likely to be contained enough to allow official interest rates to be hiked at a measured pace.

Shortly after 3:30 p.m. ET, the 10-year note jumped 1-18/32 in price to 100-18/32 to yield 4.68 percent. This was down from a 4.88 percent yield late Monday.

The 30-year bond rose 2-11/32 to 100-5/32 with a yield of 5.36 percent, down from 5.53 late Monday. Prices and yields move in opposite directions.

The two-year note added 12/32 of a point to 99-17/32 to yield 2.74 percent, and the five-year note gained 30/32 of a point to 100-16/32 to yield 3.89.

Bonds had already shot higher after a muted reading on core inflation countered speculation the Fed might have to ramp up the aggressiveness of its monetary tightening policy.

"The view that the Fed can take a measured approach is supported by the Greenspan testimony today -- he reiterated that the measured approach is really the right medicine here," Sadakichi Robbins, head of global fixed-income trading at Bank Julius Baer in New York, told Reuters.

Fed officials have recently warned that a faster pace of tightening might be needed if inflation looked to be heating up.

"The market seemed to have it in their mind that the Fed had already changed their mind, that there was a change in policy to a more aggressive pace (of rate tightening), but that did not occur," Robbins added.

Greenspan said Tuesday that "inflationary pressures are not likely to be a serious concern in the period ahead," and reiterated that the removal "of accommodation in monetary policy is very likely to be measured over the quarters ahead."

The market had already jumped early in the day after the latest reading on core U.S. inflation came in lower than many feared, also countering concerns the Federal Reserve might have to hike rates at a faster pace.

"The market was priced for accelerating inflation, but the numbers speak more of price stability," Bill Fitzgerald, head of fixed-income at Nuveen Investments, told Reuters. "That's led to a lot of short-covering in Treasurys."

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The headline consumer price index rose 0.6 percent, topping forecasts for a 0.4 percent gain. But much of that was due to higher gas prices, and excluding food and energy, the core rate rose a modest 0.2 percent as expected.

That took annual core inflation down a tick to 1.7 percent from 1.8 percent in April, a relief for the market, which had feared a rise toward the very top of the Fed's assumed comfort zone of 1 percent to 2 percent.

In the currency market, the dollar sank further against the euro and the yen. The euro bought $1.2166, up from $1.2064 late Monday, and the dollar purchased ¥109.40, down from late Monday's ¥111.20.  

-- from staff and wire reports