The Fed is unlikely to cut interest rates this week, but its statement will be analyzed for clues on possible near-term easing moves, analysts said.
Monday's sentiment has been darkened somewhat by weak US economic data and persistent pressure emanating from the trade conflict with China.
Data on the New York Fed's business index showed a record fall this month to its weakest level in more than 2-1/2 years, suggesting an abrupt contraction in regional activity and prompting an earlier fall in US yields.
The regional Fed's "Empire State" index on current business conditions tumbled to -8.6 in June from 17.8 in May.
This was the first negative reading since October 2016 when it was -9.2. Analysts polled by Reuters had forecast a reading of 10.0 for March.
"The Empire manufacturing was shockingly weak," said Stan Shipley, fixed income strategist at Evercore ISI in New York.
"So we got more bad data on top of the employment number that we got two weeks ago."
He also said the news coming out of the trade front has been disappointing. "The administration made it quite clear they don't have a lot of expectations for the G20 meeting here."
US Commerce Secretary Wilbur Ross told CNBC on Monday that President Donald Trump is ready to proceed with tariffs on the remaining $300 billion in Chinese goods in the absence of a trade deal.
"We will eventually make a deal, but if we don't the president is perfectly happy with continuing the tariff movements that we've already announced, as well as imposing new ones that has been temporarily suspended," Ross said.
Despite Monday's negative sentiment, however, Evercore's Shipley said the odds are low for an easing this week.
"The Fed will probably set the conditions where they could ease in July," said Shipley.
"That is probably tied to inflation and economic growth. So you're going to need a strong snapback in jobs, retail sales, and inflation and it doesn't look like you're going to get that."
In morning trading, US 10-year note yields rose to 2.101pc from 2.094pc late on Monday.
Yields on US 30-year bonds advanced to 2.598pc, from 2.593pc on Monday.
On the short end of the curve, US 2-year yields were up at 1.87pc from Monday's 1.851pc.