"Right now we're having communications at all levels of USA and Chinese government", Kudlow told CNBC.
Trump has also threatened to impose tariffs on all remaining Chinese imports, about US$267 billion worth, if Beijing fails to address USA demands.
At the end of the day, the only way the U.S. is likely to hit the breaks on its stance toward China is if "the voices of the United States big businesses become rowdy enough on the problems that the tariffs are causing", according to Woodward. That could entail China dropping some of its retaliatory measures and the USA agreeing not to go ahead with the planned January increase in tariffs on more than 6,000 product categories.
However, he said that several key items were lacking, meaning that the list was still "not acceptable to me yet".
China has sent a written response to U.S. demands for wide-ranging trade reforms, sources in Washington said on Wednesday, a move that could lead to negotiations to bring an end to a trade war between the world's biggest economies. "If there is a deal to be had with China it's a deal that has to be in America's interests...."
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Less than a week later, a Trump-appointed judge ordered his access restored, at least for the time being. USA Today reported that Trump hit back over Kelly's ruling, telling reporters, "people have to behave".
"If there is a deal, if and when there is a deal, it will be on President Donald J. Trump's terms".
"He was not speaking for the president, nor was he speaking for the administration", Mr Kudlow told CNBC.
Reuters reported this week that China sent the written response to US demands on Monday, ending a months-long wait. One source briefed on the offer said it was just a "rehash" of previous offers China had made. Also missing were any concessions related to what the US has long claimed are state-directed Chinese cyber-attacks on American companies to steal intellectual property, the person said. "Impossible", he said, according to Bloomberg.
Pence also said he believed that Beijing fully understands the U.S.'s position and the seriousness of its stance in the ongoing trade dispute.
Major US corporations say they are raising prices and face higher costs due to the trade war, in which Washington has imposed steep import duties on more than $250 billion in Chinese goods. "I actually think he did the president a great disservice".