President Donald Trump has said he had received a “very beautiful letter” from the North Korean leader, Kim Jong-un, and added that he could have another meeting with him.

Speaking to reporters on Friday, Trump did not say when such a meeting would take place. North Korea has been testing missiles despite a 30 June meeting between Trump and Kim at which the two agreed to revive stalled working-level talks, which have yet to resume.

Trump and Kim have met three times since last year to discuss ways to resolve a crisis over North Korea’s nuclear and missile programs, but progress has been scant on Washington’s aim of getting the North Korea leader to give up his weapons.

The recent missile tests have raised questions about the future of dialogue. Pyongyang has warned of a possible end to its freeze of nuclear and long-range missile tests in place since 2017. Trump has repeatedly pointed to that freeze as evidence of the success of more than a year of engagement with Kim.

Keen to tout his North Korea policy as a success ahead of his 2020 re-election bid, Trump has sought to play down the missile launches, saying they do not violate Kim’s pledge to forgo nuclear and long-range tests.

The US secretary of state, Mike Pompeo, said on Wednesday he was hopeful talks would resume in coming and that the US side was planning for negotiations in a couple of weeks.

A summit between Trump and Kim in Hanoi in February collapsed over a failure to narrow differences over US demands for North Korea to give up all of its nuclear weapons and Pyongyang’s demands for relief from punishing sanctions.