Thai Foreign Minister Sompong Amornvivat urged Thais in Cambodia to leave at once, mindful of the 2003 torching of the embassy and Thai businesses in Phnom Penh by a nationalist mob incensed by a row over Angkor Wat, another ancient temple.
"Thai businessmen who have no need to be in Cambodia now, please rush back to Thailand," he told reporters, adding that the military had an evacuation plan ready if needed.
In 2003, Thai commandos flew into Phnom Penh airport in the middle of the night to help evacuate 600 Thais during the riots.
Security was beefed up outside the embassy, with 20 military police armed with assault rifles standing guard.
As with other less serious clashes along the border in the past four months, each side accused the other of aggression.
On Monday, Hun Sen said a small group of Thai soldiers had strayed onto Cambodian soil and he threatened to turn the area into a "death zone" unless they withdrew by midday on Tuesday.
Singapore and Indonesia have asked both sides to show restraint.