The Fed is still in the second phase of quantitative easing, known as QE2, a $600 billion bond purchase program intended to help spur economic growth.
Bonds reached session highs after the Fed bought $7.24 billion in Treasuries maturing October 2016 to March 2018.
Stock market losses also made bonds look more appealing.
Markets expect the Fed to complete its QE2 purchases by mid-year, and many analysts say the Fed will hold the size of its balance sheet steady by reinvesting maturing assets after June to avoid a passive tightening -- an issue likely to be discussed at its April 26-27 meeting.
Fed policy makers who favor accommodation "seem to be in the lead, which leads us to expect no substantial shift in the (policy) statement," from the central bank's two-day meeting this week, said David Ader, senior government bond strategist at CRT Capital Group in Stamford, Connecticut.
The Fed policy meeting ends on Wednesday with a news conference with Fed Chairman Ben Bernanke.
Benchmark 10-year notes rose 11/32 in price, their yields easing to 3.37 percent from 3.41 percent on Thursday. The market was closed on Friday for a holiday.
"(There's a) fundamental bias that the data is indeed slowing and higher gas prices will take their toll on the consumer," Ader said.
Data on Monday showed new US single-family home sales increased more than expected in March, but there was little immediate reaction in bond prices.
Other economic reports likely to evoke somewhat muted market reaction this week include consumer confidence, durable goods and the Chicago purchasing managers index.
The Treasury's three note auctions, further refinements of monetary policy expectations, and a first report on US first-quarter gross domestic product growth, however, could add some volatility to the week's trading.
Supply from Treasury note auctions totaling $99 billion -- $35 billion in two-year notes on Tuesday, $35 billion in five-year notes on Wednesday, and $29 billion in seven-year notes on Thursday -- will be partially offset by $52.6 billion in maturing debt, leaving $46.4 billion of net cash needs, Ader said. Four Fed buybacks, month-end demand, and a persistent short-base should also support prices, he said.
Bond prices even seem to reflect some of the longer-term fiscal challenges the United States faces.
"The market reaction to the S&P outlook revision suggested that investors had already gone a good way toward pricing in the fiscal difficulties in the United States," said Robert Tipp, chief investment strategist for Prudential Fixed Income, the latter with $240 billion in assets under management.
In that context, a move that pushes 10-year yields through the recent 3.34 percent low toward the 3.25 percent range-bottom is achievable, Ader said.
Still, analysts said the technical landscape was broadly constructive with momentum favoring lower yields, albeit nearing overbought levels.
The 10-year chart shows volume built near the 3.40 percent level, which is also near the 3.41 percent 30-day moving average and a focal point, Ader said.