The more China allows its currency to weaken, the greater unease in Washington is likely to grow.

In mid-April, the U.S. Treasury warned China that the yuan (Exchange:CNY=) was too weak and expressed doubt about Beijing's determination to allow market forces to guide the value of the Chinese currency.

Since then the yuan, also known as the renminbi, has headed lower still. On Wednesday, the yuan hit its lowest level against the dollar since late 2012. It weakened to as low as 6.2674 per dollar and is down more than three percent so far this year.

"As of now it appears is if the U.S. understands the reason behind the yuan's move - i.e. China is trying to discourage speculative positioning," said Nizam Idris, managing director, head of strategy, fixed income and currencies at Macquarie Bank (ASX:MQG-AU).

"The whole adjustment in Chinese currency policy, the widening of the yuan's trading band, the U.S. welcomed that move. So, now the question is what next?," he said.

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U.S. lawmakers have long pressured Beijing to allow a faster appreciation of the yuan. They have complained in the past that Chinese efforts to hold down the value of the yuan give China an unfair trade advantage.

"Washington wants market-driven exchange rates half the time -- when the dollar is falling," said John Rutledge, chief investment strategist at Safanad in California. "They have already reacted to the falling renminbi. Expect more strong words in the months ahead."

In a commentary piece for CNBC, Yale professor and former chairman of Morgan Stanley Asia Stephen Roach said the debate over the yuan diverts attention from the more important issues affecting US-China economic ties.

"Taken to its extreme, America's accusations risk pushing the world's two largest economies down the slippery slope of trade frictions, protectionism, or something even worse," Roach said.

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Complicated

And challenging China's currency policy is not as straight forward as it seems, analysts say.

For starters, Washington wants Beijing to allow market forces to play a great role in the economy and markets and China has made steps in that direction. Last month, for instance, China widened the yuan's trading band to 2 percent from 1 percent.

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Second, China says it wants to discourage speculators from assuming the yuan is a one-way bet or in other words is only headed higher given that it has been on a path of steady appreciation since it was de-pegged from the dollar in 1995.