It was gathered that an angry crowd broke through police lines to storm parliament in the capital Nairobi before setting parts of it ablaze.
In an address on Tuesday evening, President William Ruto said all means would be deployed to thwart any attempts by dangerous criminals to undermine the security and stability of the country noting the he has also deployed the military to quell the protests.
Several groups have accused the security forces of over-reacting by using live ammunition. President of the Kenya Medical Association, Simon Kigondu, told reporters that the figure of 13 deaths was not the final number.
There have also been unverified social media reports of dozens of people being shot dead by security officers overnight, as well as reports of deaths in other areas around the country where there were protests.
Protests against an unpopular finance bill, which includes several tax rises, have been ongoing for days but they escalated on Tuesday as MPs passed an amended bill.
Protesters broke into parliament, vandalising the interior and setting parts of the complex on fire. The ceremonial mace, symbolising the authority of the legislature, was stolen. Police then opened fire with live ammunition, according to the Kenya Medical Association.