SEOUL, South Korea — North Korea said on Saturday that President Trump had sent birthday greetings to its leader, Kim Jong-un, but added that the rapport between the two leaders would not help resolve their countries’ nuclear standoff.

Ever since his first summit meeting with Mr. Kim, in Ju​ne 2018, Mr. Trump has repeatedly flaunted his “good relationship” with the North’s leader, ​ calling Mr. Kim “smart” and even going so far as to say that he and Mr. Kim “fell in love.”

The two leaders ​have also ​exchanged personal letters and dispatched special envoys to each other’s capitals, ​but talks on how to denuclearize the North remains deadlocked.

On Saturday, Kim Kye-gwan, a senior aide to Mr. Kim, confirmed that Mr. Trump had sent a personal letter to Mr. Kim for his birthday​. (Mr. Kim is believed to have turned 36 on Wednesday. ​) ​ He also acknowledged that the “personal relations” between Mr. Kim and Mr. Trump were “not bad,” but said Mr. Kim “would not discuss the state affairs on the basis of such personal feelings. ​”