
Police said they were first alerted shortly after 7am and the man has spent the day barefoot on a ledge several metres up the historic structure.
Crowds have been watching from behind a police cordon, with supporters chanting “Free Palestine” and “You are a hero”.
Negotiators boarded a fire truck lift and used a megaphone to speak with the man, but footage on social media showed him saying: “I will come down on my own terms.”
Police closed off the surrounding area including Westminster Bridge and the Houses of Parliament cancelled tours.
AFP journalists at the scene earlier said the man appeared to be bleeding from his foot.
“They are being assisted by the London fire brigade and the London ambulance service.”