S&P 500 falls 2.36 percent, while Nasdaq Composite drops 2.55 percent amid fears for central bank's independence.
Calls for more aid, support for police amid surge in violence in the Caribbean nation since the end of last year.
China is a far bigger trading partner than the US for most countries. That limits what Trump can demand, experts say.
US president calls latest controversy over defence chief's handling of military information a 'waste of time'.