WASHINGTON (Reuters) - No negotiations can be held with North Korea until it improves its behavior, a White House official said on Wednesday, raising questions about U.S. Secretary of State Rex Tillerson s offer to begin talks with Pyongyang any time and without pre-conditions.  Given North Korea s most recent missile test, clearly right now is not the time,  a White House official told Reuters. Tillerson said on Tuesday the United States was  ready to talk any time North Korea would like to talk,  appearing to back away from a key U.S. demand that Pyongyang must first accept that any negotiations would have to be about giving up its nuclear arsenal. The White House has declined to say whether President Donald Trump, who has taken a tougher rhetorical line against North Korea than Tillerson, gave approval for the overture. A day after Tillerson s comments at Washington s Atlantic Council think tank, the White House official, who declined to be named, laid out a more restrictive formula for any diplomatic engagement with North Korea.  The administration is united in insisting that any negotiations with North Korea must wait until the regime fundamentally improves its behavior,  the official said.  As the secretary of state himself has said, this must include, but is not limited to, no further nuclear or missile tests.  In his speech, however, Tillerson did not explicitly set a testing freeze as a requirement before talks can begin. He said it would be  tough to talk  if Pyongyang decided to test another device in the middle of discussions and that  a period of quiet  would be needed for productive discussions. State Department spokeswoman Heather Nauert on Wednesday appeared to walk back part of Tillerson s proposal, saying there would have to be a suspension of North Korean nuclear and missile tests for an undefined length of time before any talks could take place.  And we certainly haven t seen that right now,  she told reporters, insisting Tillerson had not unveiled a new policy and was  on the same page  as the White House. Tensions between Washington and Pyongyang over North Korea s weapons advances have grown this year and recent exchanges of bellicose rhetoric have fueled fears over the risk of military conflict. Tillerson s relationship with Trump has been strained by differences over North Korea and other issues, and he has seen his influence diminished within the administration. Senior administration officials said late last month that Trump was considering a plan to oust Tillerson, though the secretary of state has dismissed that. Tillerson said in his speech that Trump  has encouraged our diplomatic efforts.  Trump, however, tweeted in October that Tillerson was  wasting his time  trying to negotiate with North Korea. Tillerson s overture came nearly two weeks after North Korea said it had successfully tested a breakthrough intercontinental ballistic missile (ICBM) that put the entire United States mainland within range. North Korea has made clear it has little interest in negotiations with the United States until it has developed the ability to hit the U.S. mainland with a nuclear-tipped missile, something most experts say it has still not proved. In Beijing, Chinese Foreign Ministry spokesman Lu Kang said following Tillerson s speech that China welcomed efforts to ease tension and promote dialogue to resolve the North Korea standoff. Russia also welcomed Tillerson s statement, the Interfax news agency cited Russian Deputy Foreign Minister Sergei Ryabkov as saying. Ahead of Tillerson s speech, North Korean leader Kim Jong Un vowed to develop more nuclear weapons while personally decorating scientists and officials who contributed to the development of Pyongyang s most advanced ICBM, state media said on Wednesday. Despite that, a U.S. official, speaking on condition of anonymity, said Tillerson s remarks followed speculation North Korea might be willing to talk having announced it had completed a major milestone with last month s missile test and suggested he was trying to take advantage of a potential opening. 