The benchmark 10-year Treasury's yield fell to its lowest since September 2017 overnight, near 2pc, after St.
Louis Federal Reserve President James Bullard said a rate cut "may be warranted soon" given weak US inflation and the threat to economic growth posed by global trade tensions.
The Japanese yen has been the main beneficiary from a shift towards assets investors deem a safer bet. It rose 0.2pc to 107.845 yen per dollar, its strongest since mid-January.
That hurt the dollar, which against a basket of currencies was down 0.1pc to a three-week low, falling below 97 for the first time since April 18.
"As long as it (the dollar) is at the centre of the trade conflict, US yields fall due to concerns about real economic effects and the market is literally calling out for rate cuts, there are no positive arguments supporting the dollar," Commerzbank analyst Antje Praefcke said.
Other strategists were less bearish on the dollar, arguing that rate cuts had already been priced into the currency and noting that if global growth does worsen, the dollar should benefit from its safe-haven credentials.
The euro rose 0.3pc to $1.1274, its highest since April 18, helped by dollar weakness.
The European Central Bank meets on Thursday, and investors are also eyeing flash euro zone inflation data due at 0900 GMT.
Analysts remain cautious on its prospects.
"Considering the euro zone's close ties with the Chinese economy, the euro is one of the currencies that stands to be most affected by a Chinese economic downturn - a risk associated with the escalating US-China trade war," said Tokyo-based Junichi Ishikawa, senior FX strategist at IG Securities.
Elsewhere, the Australian dollar was little changed after the Reserve Bank of Australia cut interest rates to a record low of 1.25pc, as expected.
The pound rose 0.2pc to $1.2684, up from a five-month trough of $1.2560 set on Friday.
Sterling has fallen on the prospect of a eurosceptic prime minister replacing Theresa May who could push for a more decisive break from the European Union, Britain's largest trading partner.