NEW YORK (Reuters) - The dollar gained on Monday after the United States and Mexico reached a deal to avoid tariffs, while the euro faltered after sources said European Central Bank policymakers were open to cutting interest rates should economic growth slow.

FILE PHOTO: U.S. Dollar banknotes are seen in this photo illustration taken February 12, 2018. REUTERS/Jose Luis Gonzalez/Illustration

On Friday, Mexico agreed to rapidly expand an asylum programme and deploy security forces to stem the flow of Central American migrants to the U.S. border.

U.S. President Donald Trump had threatened to impose 5% import tariffs on all Mexican goods starting on Monday if Mexico did not commit to do more to tighten its borders.

“The news that tariffs on Mexico will now be averted is the main reason the dollar had a good bounce overnight,” said Richard Franulovich, head of FX strategy at Westpac Banking Corp in New York.

Last week, the greenback weakened on concerns that trade disputes would hurt the global economy. U.S. jobs data also was weaker than expected, feeding expectations the Federal Reserve would cut U.S. interest rates.

Jobs data on Monday showed a brighter outlook, with U.S. job openings falling slightly in April as hiring surged to a record high.

The U.S.-China trade war and worries that Trump will slap tariffs on Japan and Europe are likely to keep investors averse to loading up on riskier assets.

“I think the market psyche has been rattled and this is increasingly going to be a headwind for sentiment,” said Franulovich. “There is still the outstanding issue with China, and on top of that many other countries that are in his cross hairs.”

Trump said on Monday he was ready to impose another round of punitive tariffs on Chinese imports if he does not reach a trade deal with China’s president at a Group of 20 summit later this month.

The euro dipped after two sources familiar with the ECB’s policy discussions said on Sunday that a rate cut was firmly in play if the bloc’s economy stagnates again after expanding by 0.4% in the first quarter.

The single currency soared last week after the ECB said rates would stay “at their present levels” until mid-2020 instead of hinting at rate cuts, as some expected.