SEOUL: North Korean leader Kim Jong Un has ordered more solid-fuel rocket engines, state media reported on Wednesday, as he pursues nuclear and missile programs amid a standoff with Washington, but there were signs of tension easing.

The report carried by the KCNA news agency lacked the traditionally robust threats against the United States after weeks of unbridled acrimony, and U.S. President Donald Trump expressed optimism about a possible improvement in relations.

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

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

The KCNA report, about a visit by Kim to a chemical institute, came not long after U.S. Secretary of State Rex Tillerson appeared to make a peace overture, welcoming what he called recent restraint shown by the reclusive North.

Kim was briefed about the process of manufacturing intercontinental ballistic missile (ICBM) warhead tips and solid-fuel rocket engines during his tour of the Chemical Material Institute of the Academy of Defence Science, KCNA 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 beginning of last year, significantly raising tension on the heavily militarized Korean peninsula and in defiance of U.N. Security Council resolutions. Two ICBM tests in July resulted in a new round of tougher global sanctions.

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