North Korea has not conducted a missile test for 53 days, the longest such lull in testing this year. North Korean state media has not commented on Trump's arrival in the South.
South Korea's spy agency said last week that North Korea may be preparing another missile test, raising speculation that such a launch could be timed for Trump's trip to the region.
U.S. officials have said privately that intercepting a test missile is among options under consideration, though there is disagreement within the administration about the risks.
The South Korea leg of Trump's trip is an effort to present a united front despite differences with Moon over how to confront North Korea, as well as Trump's complaints over the two countries' trade agreement and South Korean defense spending.
Trump has criticized Moon over his support for diplomatic engagement with Pyongyang — something the U.S. president once called "appeasement" — and has threatened to pull out of a free trade pact between the two countries.
"Hopefully that will start working out, and working out so that we create a lot of jobs in the United States which is one of the reasons that I'm here," Trump told reporters, referring to trade issues between the two countries.
Trump has rattled some U.S. allies with his vow to "totally destroy" North Korea if it threatens the United States, for deriding Kim as a "Rocket Man on a suicide mission" and for dismissing as pointless any diplomatic engagement with Pyongyang.