Meanwhile, interest rates have moved to the fore, with the bench mark U.S. 10-year Treasury yield reaching 3 percent for the first time in four years Monday. It continued to move higher Tuesday, touching a high of 3.03 percent.

The dollar 's move comes after worries that the U.S. would barrel forward with Trump's threat to put tariffs on $150 billion in Chinese goods, igniting a trade war. But some of the harshest talk has died down, and the Trump administration also has said there's been progress in talks to renegotiate the North American Free Trade Agreement between the U.S., Canada and Mexico.

The dollar index was up a half percent Wednesday, to above 91 and it has gained nearly 2 percent in the past week.

The dollar has been moving higher, crushing doubters and trading more on rising U.S. interest rates than on President Donald Trump's trade threats.

"I think we have this tension between some big long-term negatives and on the other hand, the rates move is a powerful force," said Jens Nordvig, CEO of Exante Data. Nordvig said the dollar, which was heavily shorted, should continue to move higher over the next month as traders exit those positions.

Treasury Secretary Steven Mnuchin and others, including U.S. Trade Representative Robert Lighthizer and White House top economic adviser Larry Kudlow travel to China next week.

"The trip that's been arranged to China has calmed down fears," Nordvig said. "We also think the NAFTA deal is very close."

Expectations are also rising for Federal Reserve interest rate hikes, with odds of a fourth rate hike for 2018 gaining momentum. The Fed meets next week, but it is not expected to take any action on rates, and it will not update its interest rate forecast until its June meeting.

"Everybody was giving up on the interest rate story, and now it's kicked in with a vengeance," said Marc Chandler, the head of fixed income strategy at Brown Brothers Harriman.

Chandler said the Fed may not make it clear that it intends a fourth rate hike for 2018 until it gets closer to its December meeting.

The European Central Bank meets Thursday, and it is also not seen taking any rate action as it is expected to wind down asset purchases this year. Chandler said ECB President Mario Draghi will make no waves on the currency front, and he notes that the euro is lower against the dollar but on a trade weighted basis, it's firming against other currencies.

'We're seeing cyclical fundamentals turn to favoring the U.S. and that is a recipe for the dollar to strengthen, and we think it continues for awhile," said Ben Randol, Bank of America Merrill Lynch G-10 currency strategist. "One thing that we've seen is relative central bank expectations, which were a catalyst for the euro higher at the beginning of the year, have reached cyclical limitations."

Randol said the euro, at 1.2176 to the dollar Wednesday, could fall to 1.15 in the second quarter. He said the dollar index, which includes the euro, yen and other currencies, should also move higher. He expects dollar/yen to reach 112, from its current 109.34.

"That index is trading somewhere around 8 to 10 pct below interest rate differential implied fair value," Randol said, adding the greenback may not make that entire move.

Chandler said, however, there are still risks from trade. May 1 is the deadline for tariff exemptions on steel and aluminum imports from Mexico, Canada and the EU. "I think people are looking at the wrong thing," he said. "People are looking at China, but more immediate is the exemption."

Chris Krueger, Washington policy strategist for Cowen, notes that the Mnuchin trip to China is the day after the steel exemptions expire, and the officials are expected to try to de-escalate the worries about tariffs on China.

"What is clear is that this Administration is not limited by any of the trade norms that have been established since World War Two. The only thing predictable is their unpredictability," Krueger wrote in a note.