Indonesia "deeply regrets" the order by United States President Donald Trump to suspend refugee arrivals and barring visas for travellers from seven Muslim-majority countries.

While accepting that the executive order is the right of the US government, "we believe this will have a negative impact in our global fight against terrorism and in tackling the issue of refugees", Foreign Ministry spokesman Arrmanatha Nasir told The Straits Times via text messages yesterday.

"It is a mistake and a slippery slope to link the issue of radicalism and terrorism with any particular religion," he said.

"Efforts to fight against terrorism must be done by advancing international cooperation and by addressing the root causes of terrorism," he added.

Indonesia, the world's most populous Muslim nation, will continue to "closely follow" the policies made by the new US administration, he said. Indonesia isn't among the seven nations whose citizens face restrictions.

Indonesian Foreign Minister Retno Marsudi told Reuters: "We have deep regrets about the policy."

The new policy has led the Indonesian Foreign Ministry to issue an advisory to remind its citizens residing in the US to keep calm, respect local laws and maintain public order. A 24-hour hotline has also been activated in several US cities.

Ms Retno has instructed all Indonesian representative offices in the US to anticipate and ensure maximum safety and protection for its citizens, another ministry official, Mr Lalu Muhammad Iqbal, said.

Mr Lalu was concerned about the order on Border Security and Immigration Enforcement Improvements, saying among its key components is the arrest and deportation of illegal immigrants previously protected by the government in a number of "sanctuary" cities there.

He said the US government's decision, while it must be respected, "does not contribute to resolving global problems together, whereas we are counting on the US to show its leadership".