NEW YORK (CNNMoney.com) - Bond prices rose Tuesday, pushing the benchmark back below 5 percent, as investors took in a tame inflation report and cheered signs that an end to the Federal Reserve's rate hiking campaign may be near.

The dollar weakened against the euro and the yen.

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The 10-year Treasury rose 5/32 to 96-09/32 to yield 4.98 percent, down from 5.01 late Monday. The benchmark yield surpassed the 5 percent mark for the first time since June 2002 last Thursday. Bond prices and yields move in opposite directions.

The 30-year bond rose one tick to 91-7/32 to yield 5.07 percent, down from 5.08 percent in the previous session.

The five-year note rose 7/32 to yield 4.87 percent. The two-year note added three ticks, yielding 4.84 percent.

The benchmark Treasury yield has jumped nearly three quarters of a percentage point in the past three months as investors have bet the Fed might raise short-term rates more than originally expected. But minutes from the Fed's March 27-28 meeting, released on Tuesday, showed policymakers eyed an end to central bank's now 21-month old rate-boosting campaign.

"Most members thought that the end of the tightening process was likely to be near, and some expressed concerns about the dangers of tightening too much, given the lags in the effects of policy," the minutes said. (Read the minutes.)

"You are getting the rally in Treasuries because the minutes imply a little less tightening than what the market had anticipated," Keith Hembre, chief economist with FAF Advisors in Minneapolis, told Reuters.

Treasuries also got a boost early in the session after the Labor Department reported the so-called core Producer Price Index, a key measure of inflation that strips out energy and food costs, rose only 0.1 percent in March, marking its smallest gain in four months.

Bond traders hate inflation since it erodes the value of their fixed-interest paying investments.

Sentiment also picked up on some economic weakness in the housing market. The Census Bureau said housing starts fell to an annual rate of 1.96 million in March, compared to an upwardly revised 2.13 million pace in February. Economists polled by Briefing.com predicted the rate would slip to 2.03 million for March.

The euro bought $1.2323, up from $1.2256 late Monday, while the dollar bought ¥117.25, down from ¥117.83 the previous session.

--from staff and wire reports

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Long-term bond rates are finally rising. How far will they go? Click here.