HONG KONG—China and Taiwan’s currencies both slipped against the U.S. dollar amid a broad rally for the greenback in Asian trading Monday, as U.S. President-elect Donald Trump again criticized Chinese currency and trade policy.

The yuan was down just 0.1% against the dollar in onshore trading after China’s central bank had earlier guided the currency a touch weaker. The People’s Bank of China set the daily midpoint for the dollar-yuan pair at 6.8870 on Monday, compared with 6.8794 on Friday. The Chinese currency is allowed...