The dollar edged up slightly on Tuesday after falling to its lowest in more than two months at the start of the week, buoyed by safe-haven flows after US President Donald Trump said tariffs on Mexico and Canada would proceed as planned.

The firmer dollar in turn left the euro off a one-month high at $1.0476, with future gains in the single currency likely to hinge on how soon a coalition government can be formed in Germany following the election victory of the country's conservatives.

Trump on Monday said that tariffs on Canadian and Mexican imports are "on time and on schedule" despite efforts by the countries to beef up border security and halt the flow of fentanyl into the US ahead of a March 4 deadline.

Many had hoped the top two US trading partners could persuade Trump's administration to further delay tariffs that would apply to over $918 billion worth of US imports from the two countries, from autos to energy.

His comments spurred a rush to safety assets like gold and US Treasuries, with the dollar also a beneficiary of some of those risk-off moves.

Sterling drifted from Monday's two-month high and last fetched $1.26385. The Aussie ticked up 0.07 percent to $0.6354, but was some distance away from a 2-1/2-month high hit last week.

The dollar index steadied at 106.59, rebounding from a more than two-month trough of 106.12 hit in the previous session.