This marks at least the second time China has denied a request by the United States this month, having earlier rejected a request for two US Navy ships to visit Hong Kong, as the political crisis in the former British colony deepened.
US President Donald Trump said on April 4 that the two sides could have a deal worked out in about four weeks. On Thursday, he said he would soon host Chinese President Xi Jinping at the White House - a meeting seen as needed to cement an agreement.
Trump, in remarks to White House staff, parents and children gathered on the lawn for Take Your Children to Work Day, did not indicate when the meeting might take place or what would be on the agenda. He has suggested in the past that Xi would travel to the US for a signing ceremony.
Captain James Fanell, a former US Navy intelligence chief, told Reuters that China now has "the most advanced ballistic missile force in the world" and has "the capacity to overwhelm the defensive systems we are pursuing."
On Wednesday, Beijing accused Washington of bullying and warned it would hit back after the Trump administration raised the stakes in their trade dispute, threatening 10 percent tariffs on $200 billion of Chinese goods.