The UN estimates the move will cost North Korea $1 billion per year.
Trade between the two countries has been greatly affected as a result of Bangkok's adherence to the UNSC's resolution on North Korea.
The missile tests led Washington to propose a new resolution at the United Nations, which was approved by the Security Council on Saturday. "But we need to abide by the United Nations resolution", said Foreign Minister Don Pramudwinai.
Tillerson was the highest-ranking US official to visit Thailand since a coup there in 2014.
In 2014 the two countries shared trade worth $126 million, according to Thailand's Ministry of Foreign Affairs, almost a three-fold increase since 2009.
One week earlier, North Korea launched the second of two missiles that officials said would be capable of striking the USA mainland. Both countries have maintained diplomatic ties for 42 years.
Tillerson would not give a timeline on North Korea's actions that could satisfy the United States, but said "we'll know when we see it".
North Korea has in recent weeks tested two intercontinental ballistic missiles, and experts believe the tests show the missiles have the capability to reach parts of the United States.
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The one-day drop-in comes as Washington reboots its relationship with Thailand under President Donald Trump, whose administration has enraged rights groups by cosying up to strongmen around the globe.
Since the overthrow of the civilian government in Thailand by a military junta, ultra-royalist, the gatherings of a political nature, remain prohibited, among other restrictions on freedom of expression, criticised by Washington after the coup.
On Prayut's upcoming visit to Washington, Weerachon said Tillerson hoped he would welcome the Thai prime minister and his delegates to the White House soon as both officials continued their discussion on the date of the state visit.
On the South China Sea issues and crisis on the Korean Peninsula, Prayut told Tillerson of Thailand's readiness to extend cooperation and support to the United States.
"We talked about it in the discussion we had with Minister Lavrov yesterday - and trying to help them understand just how serious this incident had been and how seriously it had damaged the relationship between the USA and the American people and the Russian people, that this had created serious mistrust between our two countries and that we simply have to find some way to deal with that", Tillerson said.
Tillerson is also slated to pay respects to Thailand's late King Bhumibol Adulyadej, who has been lying in state at the Grand Palace since his death in October 2016.
Tillerson is scheduled to travel to Kuala Lumpur to meet Malaysian Prime Minister Najib Razak late Tuesday.
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