SEOUL:  North Korean leader Kim Jong Un ordered the production of more solid-fuel rocket engines and rocket warhead tips, the North's official media said on Wednesday 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.

US President Donald Trump also expressed cautious optimism about a possible improvement in relations with the North, after months of mounting tension over its weapons programmes.

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.

North Korea has conducted two nuclear tests and dozens of missile tests since the start of last year, significantly raising tensions on the heavily militarised Korean peninsula. Two tests of intercontinental ballistic missiles in July resulted in a new round of tougher global sanctions.

The last missile test on July 28 put the US mainland in range, prompting heated exchanges that raised fears of a new conflict on the peninsula.

Tillerson, however, noted what he called the restraint the North had shown lately and said on Tuesday he hoped a path could be opening for dialogue some time in the near future.

Later on Tuesday at a campaign rally in Phoenix, Arizona, Trump said of Kim: "I respect the fact that he is starting to respect us."

"And maybe - probably not, but maybe - something positive can come about."

South Korea and the United States are conducting an annual joint drill involving computer simulations of a possible war on the Korean peninsula, exercises that the North routinely describes as preparation for invasion. The drills started on Monday and will run through to August 31.

South Korea will also conduct a voluntary civil defence drill across the country later on Wednesday.

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 US Pacific territory of Guam after US President Donald Trump earlier warned North Korea it would face "fire and fury" if it threatened the United States.

New US sanctions announced on Tuesday target Chinese and Russian firms, as well as individuals, for supporting Pyongyang's weapons nuclear and missile programmes.