Iran has stayed the executions of protesters, President Donald Trump said, quoting "very important sources on the other side," but tensions continued across the Middle East as the possibility of US military action against Tehran remains.

"They've said the killing has stopped and the executions won't take place -- there were supposed to be a lot of executions today and that the executions won't take place -- and we're going to find out," Trump told reporters at the White House on January 14.

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"We've been told on good authority, and I hope it's true."

Iranian authorities have waged one of the most brutal crackdowns ever after people across the country took to the streets in anti-government protests seen as one of the biggest challenges to clerical rule since the 1979 Islamic Revolution.

The independent US-based rights monitor HRANA said that according to its confirmed and verified data on January 14 the death toll in the protests had risen to 2,435 protesters, with more than 18,000 others arrested. But it and other sources say the real number of those killed is likely several times higher.

In light of the reports of the violent crackdown, Trump has warned several times that the United States may intervene to halt the killings while urging Iranians to continue their protests.