US President Donald Trump expressed cautious optimism last night about a possible improvement in relations with North Korea after months of mounting tension over its weapons programs.

Trump made the remarks to thousands of his supporters in Phoenix, Arizona. 

"Kim Jong Un, I respect the fact that I believe that he is starting to respect us. I respect that fact very much. Respect that fact. And maybe, probably not, but maybe, something positive can come about," he said.

North Korea has conducted two nuclear tests and dozens of missile tests since the start of last year.

Washington says the aim of any future talks must be denuclearisation, something Pyongyang has rejected as long as the United States maintains a "hostile policy" towards it.

KIM ORDERS MORE ROCKETS

Meanwhile, North Korean leader Kim Jong Un has ordered the production of more solid-fuel rocket engines and rocket warhead tips, the North's official media said in a report otherwise lacking threats against Washington after weeks of heightened tension.

A report about Kim's visit to a chemical institute came not long after US Secretary of State Rex Tillerson appeared to make a peace overture to Pyongyang, welcoming what he called the recent restraint shown by the reclusive North. 

He instructed the institute to produce more solid-fuel rocket engines and rocket warhead tips

Kim was briefed about the process of manufacturing intercontinental ballistic missile warhead tips and solid-fuel rocket engines during his tour of the Chemical Material Institute of the Academy of Defence Science, the North's official KCNA news agency said.

"He instructed the institute to produce more solid-fuel rocket engines and rocket warhead tips by further expanding engine production process and the production capacity of rocket warhead tips and engine jets by carbon/carbon compound material," KCNA said.   

The KCNA report said Kim had given "special thanks and special bonus" to officials of the institute, calling them heroes. A photograph showed Kim in a grey pinstriped suit, smiling before a large flow chart that described some kind of manufacturing process.

However, there was none of the fiery rhetoric of recent weeks, when Kim threatened to fire missiles into the sea near the U.S. Pacific territory of Guam after U.S. President Donald Trump earlier warned North Korea it would face "fire and fury" if it threatened the United States. 

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