Benchmark 10-year bond yields in Germany fell one basis point to -0.2930pc, moving further away from a three-week high of -0.26pc reached last week.
Comparable yields in France and Belgium were down a similar amount.
"It is basically the Fed, ECB and the tariffs that is keeping everybody on edge with all these headlines on the trade front not removing the broader confusion," said Benjamin Schroder, a rates strategist at ING Bank in London.
Another round of U.S. tariffs on Chinese goods is due to take effect on Dec. 15, and Britain holds an election on Thursday.
Both supported demand for fixed-income assets after some mixed economic data from Germany in recent days.
The Fed concludes a two-day meeting on Wednesday, with last Friday's U.S. jobs report expected to give the U.S. central bank all the reason it needs not to cut interest rates further.
Strategists at Mizuho expect Fed Chairman Jerome Powell to imply two-way risks to the Fed's outlook.
Money markets expect no change at the ECB meeting.
Signs that the worst may be over for the euro zone economy buys the ECB's Christine Lagarde some time, analysts say.
With currency market volatility near record lows, demand for peripheral European debt remained supported, with yields in 10-year Italian bonds holding near a two-week low of 1.345pc.