The Canadian dollar dropped against its major counterparts in the New York session on Tuesday, as the nation's consumer inflation slowed to a two-year low in May, reducing expectations for another rate hike next month.

Data from Statistics Canada showed that the consumer price index rose 3.4 percent year over year in May, following a 4.4 percent increase in April. The reading matched expectations.

The CPI rose 0.1 percent on a seasonally adjusted monthly basis in May, after a 0.5 percent increase in the previous month.

Core CPI, excluding food and energy, eased to 0.2 percent from 0.3 percent last month.

Oil prices traded lower as concerns over possible supply disruptions due to political instability in Russia eased and European Central Bank President Christine Lagarde reiterated that the central bank will continue to increase rates in July.

The loonie fell to 4-day lows of 1.3189 against the greenback and 0.8838 against the aussie, from its prior multi-month highs of 1.3116 and 0.8763, respectively. The next possible support for the currency is seen around 1.33 against the greenback and 0.91 against the aussie.

The loonie was down against the euro, at a 4-day low of 1.4461. If the currency falls further, 1.46 is likely seen as its next support level.

The loonie eased to 108.75 against the yen, from an early multi-month high of 109.50. The currency may locate support around the 103.5 level.

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