The dollar was steady against the euro and a basket of major currencies after the United States and Mexico agreed to overhaul the North American Free Trade Agreement, boosting optimism for an easing of global trade tensions.

The agreement put pressure on Canada to consent to new terms in order to preserve a three-nation pact, which would ultimately dial back the economic uncertainty caused by US President Donald Trump's repeated threats to ditch the 1994 accord.

Shusuke Yamada, currency and equity strategist at Bank of America Merrill Lynch in Tokyo, said Canada's readiness to join the deal remained something to watch though it was difficult to gauge when investors expected a breakthrough.

“It would be positive for the Canadian dollar, Mexico peso, these currencies that have been sold on the back of higher trade tensions,” Yamada said. “Overall, that would be negative for the Japanese yen and the US dollar. That's positive for the risk assets in general,” he said.

The dollar index, which measures the greenback's performance against six other currencies, was nearly flat on Tuesday following the two previous sessions of losses. The index edged 0.05 per cent higher to 94.834 as of 0135 GMT, making up small losses earlier.

The dollar has fallen more than 2 per cent since hitting a high not seen in over a year on Aug 15, amid US President Donald Trump's criticism of the Federal Reserve for raising interest rates at a time when the US government was trying to stimulate the economy.

On Tuesday, the euro was down 0.04 per cent at $1.1674 as of 0135 GMT giving up earlier gains. The common currency was about 0.1 per cent higher against the yen at 129.895 yen per euro. The euro extended five straight sessions of gains in which it has gained about 2.7 per cent against the Japanese currency. “Cross-yen pairs like euro/yen...have been a function of risk assets,” Yamada said, adding that a de-escalation of trade tensions normally supports cross-yen trades.

Against the yen, the dollar was 0.2 per cent higher at 111.28 yen per dollar. The Canadian dollar was about 0.1 per cent higher at $1.297 after slipping almost half a percent on Monday. The Mexican peso edged about 0.1 per cent lower at 18.795 per dollar. On Monday, the peso closed about 0.8 percent higher after initially rising about 1.2 per cent on the news that the United States and Mexico had reached agreement.

China's offshore yuan traded about 0.1 per cent lower at 6.8017 per dollar as of 0138 GMT. It was not far off 6.7818, its strongest since July 31 touched on Monday after the central bank late last week revived a “counter-cyclical factor” in its daily fixing to support the currency.