At least three student activists have been taken to hospital after they were run over by the police van, protest leader Renato Reyes said.
Footage showed the van repeatedly ramming the protesters as it drove back and forth after activists surrounded the vehicle and started hitting it with wooden batons seized from police.
The van suddenly charged backwards then shot forward twice over a space of about 20 meters (60ft), careening through the scattered protesters.
A few were hit but somehow managed to stand. Some screamed in surprise while others threw stones at the van and shouted.
"There was absolutely no justification for it," Mr Reyes said of the violent police dispersal of about 1,000 protesters.
"Even as the president vowed an independent foreign policy, Philippine police forces still act as running dogs of the US."
Police lobbed tear gas and arrested at least 23 protesters who broke through a line of riot police and threw red paint at the officers and a US government seal at the start of the rally at the seaside embassy compound.
A fire engine doused the protesters with water to push them back, but they took hold of the water hose and confronted the outnumbered police with rocks and red paint.
After breaking through the police corridor, they scribbled "US troops out now" and other slogans at the embassy's tall fence with red paint.
The protesters, consisting of students, workers and tribespeople, were demanding an end to the presence of visiting US troops in the Philippines and to support a call by President Rodrigo Duterte for a foreign policy not dependent on the US, the country's long-time treaty ally.
The activists came from the largest left-wing umbrella group called Bayan (Nation), which has organised regular anti-US protests in front of the embassy for decades — most of which are peaceful.
The violence happened as the police and Mr Duterte are under increased international scrutiny for their alleged role in the killings of thousands of drug suspects and pushers as part of the president's war on illegal drugs.
Additional reporting by PA
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