Prime Minister Srettha Thavisin's comments came amid a public row triggered earlier this month when monarchy-reform activist Tantawan "Tawan" Tuatulanon, 22, did a live broadcast on her Facebook account showing her arguing with police officers who were blocking cars for a passing royal motorcade.
The monarchy, which many Thais consider sacrosanct, is officially above politics and constitutionally enshrined to be held in "revered worship".
Insulting the monarchy carries penalties of up to 15 years in prison under Article 112 of Thailand's criminal code.
Several local media reported that the car Tantawan was riding in, prior to the video, was allegedly honking and trying to overtake the motorcade carrying Princess Sirindhorn, the sister of King Maha Vajiralongkorn, on an expressway in Bangkok.
The police are considering taking legal action against Tantawan and fellow activist over the February 4 motorcade incident, Police Chief Torsak Sukvimol told reporters on Monday.
Tantawan, who already is facing royal insult charges for previously discussing royal motorcade issue, apologising for driving recklessly on February 4 in a Facebook post on Monday, and denied that her car was trying to harass or block the royal convoy.
On Saturday, a group of ultra-royalists angered by the motorcade incident clashed with Tantawan and her fellow activists at a skytrain station as they were planning to hold a press conference in front of a shopping mall in central Bangkok.
Prime Minister Srettha condemned the violence and urged the activists to seek to discuss the issue in "safe spaces".
"We have parliament, we have academics, we should discuss the issue in appropriate venues," he said. "Not in venues that are confrontational, like malls or public places, those are inappropriate."
Srettha also stressed that the government must prioritise the safety of the royal family and said he had discussed the matter with the police chief and other security officials.
Just a few years ago, even discussing royal motorcades in public would have been almost unthinkable.
A youth-led political movement that emerged in 2020 and broke traditional taboos by calling for the reform of the powerful monarchy has previously criticised the blocking of traffic for royal motorcades.
The Thai government in late 2020 said the king was concerned and the police had adjusted security protocols to reduce disruption for the public.
