Thai-Malaysian Regional Border Committee secretary Adisak Prachakittikul said Thailand did not see any problem with Malaysia's plan because the construction would not encroach on Thai territory.
Kelantan state is opposite Narathiwat's Sukhirin, Sungai Kolok, Tak Bai and Waeng districts.
"We believe it will be good for the countries in preventing the smuggling of contraband goods," Col Adisak said.
Col Adisak said Thailand had a similar plan to build a wall and fence along the border to prevent smuggling and other forms of border crime. "The Internal Security Operations Command's Region 4 is conducting an aerial survey to assess the feasibility of a wall and fence on the Thai side," he said.
Army chief Prayuth Chan-ocha said the construction of border walls and fences is standard international practice.
On Sunday, the New Straits Times newspaper reported on its website that Malaysia's Home Ministry plans to declare areas connected to the 121-kilometre Kelantan border as security zones, to prevent trans-national crime.
Home Minister Ahmad Zahid Hamidi said the wall and fence programme should be speeded up, as the problems in Kelantan were worse than in other states.
"The idea was proposed by the state police, and I agreed it should proceed quickly," he said after visiting the Kelantan police contingent headquarters on Saturday.
"I will apply for a special allocation from the prime minister, as he understands the limitations faced by the police and other enforcement agencies.
"I think a long-term solution to the problem is to build a wall and declare the border as a security area."
Dr Zahid said the wall and fence would deter drugs and firearms smuggling as well as stop criminals from fleeing across territories.
He said residents living along the river would not be relocated, but all illegal jetties would be destroyed and more policemen would be assigned to the area.
"I realise the livelihoods of people living along the border will be affected by the proposed plan," Dr Zahid said.
"But we have to stop the smuggling of firearms and drugs and prevent criminals escaping across the border. The country's security must be a priority."