Protests erupted in Iran on November 15 after an announcement that petrol prices were going up by as much as 200 per cent with immediate effect.
"Iran is killing perhaps thousands and thousands of people right now as we speak," Trump told reporters in London ahead of a Nato summit.
"That's why they cut off the internet. They cut off the internet so people can't see what's going on. And frankly, I don't know how you get in there, I don't know how you do your business but the press ought to get in there and see what's going on."
Rouhani praises Pakistan’s role for regional peace
Trump added: "The word is that thousands of people are being killed in Iran that are protesting.
"Not just small numbers, which are bad; big numbers, which are really bad and really big numbers."
Asked if there was more that the United States could do, he replied: "I'd rather not say right now.
"It's a terrible thing and I think the world has to be watching.
"But many, many people are being killed in Iran right now for protesting. For the mere fact that they're protesting."
Banks and petrol stations were torched and shops looted in the violence which was quickly quashed by authorities who also imposed a week-long, near-total internet blackout.
London-based human rights group Amnesty International said on Monday that at least 208 people were killed in the crackdown.
Iran on Tuesday rejected as "utter lies" unofficial casualty figures given for the street violence.
The authorities have not yet provided any overall death toll for the unrest.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ