Most regional equity markets rose after Mexico agreed to take strong measures to curb illegal immigration, as the prospect of another trade war had prompted heavy selling over the past week.
The US dollar was up about 0.3pc.
Markets had priced in slightly more than a 50pc probability that rates would be cut 25 basis points by the end of July and one more cut would follow by the end of the year, according to the CME Group's FedWatch Tool.
Weaker US employment data on Friday had also raised expectations for an interest rate cut.
Policy easing by the Fed would drive capital flows to regional markets on the prospect of better yields.
"It sort of diminished the urgency for the Fed to move on the rate cut because you price out the downside risk with regards to the tariffs.
From that perspective, it seems that some of the dollar selling on the back of lower US rates could be unwound this week," said Chang Wei Liang, forex strategist at Mizuho Bank.
Sentiment was rattled early in the Asian trading day after Chinese imports in May slid a worse-than-expected 8.5pc from a year earlier, pointing to weakening demand from the world's second-largest economy.
Exports saw a surprise return to growth although analysts said this could be due to front-loading by exporters to avoid higher US tariffs.
The Chinese yuan was among the biggest losers for the day, shedding about 0.3pc to the dollar.
Increased trade tensions have battered the currency, which traded at its weakest level in more than six months.
"We don't see too much of a relief rebound partly because US policy capriciousness has become a lot more damaging to market sentiment," Chang added.
A Reuters poll last week found that market participants were broadly bearish on most Asian currencies as the US-China trade conflict showed no signs of abating. Investors will now look to any developments at a G20 leaders' summit late this month.
The South Korean won shed about 0.2pc, while the Philippine peso dropped 0.4pc. Most other regional units traded in a flat-to-low range.
RUPIAH GAINS
The Indonesian rupiah led gains, rising about 0.32pc to the dollar after markets were closed last week for the Eid al-Fitr holidays.
Inflation in Southeast Asia's largest economy accelerated more than expected in May, cooling expectations for fiscal policy easing in the country, given that the figure was well within Bank Indonesia's target.
Mizuho's Chang said that the country may be more insulated to global trade headwinds than its peers due to its reliance on domestic demand, rather than exports.
Chang also noted that the continuance of economic reform policies would spur interest in the country, after incumbent President Joko Widodo retained power.
The following table shows rates for Asian currencies against the dollar on Monday.