Protesters on Tuesday morning also occupied the rooftop of subcontractor Guardtech Group in Suffolk.
A spokesperson for Avon and Somerset Police said officers were called to the Bristol site at around 06:30 BST and had responded to a protest involving two people.
“We’re committed to facilitating people’s right to peaceful protest, but will not tolerate any criminal behaviour,” they added.
As of 13:00, the protesters remained at the site.
Palestine Action is seeking a legal challenge against the government’s bid to proscribe it, with a hearing expected on Friday to decide whether the ban can be temporarily blocked, pending further proceedings to decide whether a legal challenge can be brought.
A Suffolk Police spokesperson also said officers and specialist negotiators were on the scene in Brandon “to bring this to a conclusion” and ensure the safety of those in the area.
Israel launched its military campaign in Gaza in response to Hamas’s 7 October 2023 attack, in which about 1,200 people were killed and 251 others were taken hostage.
Since then, 56,500 people have been killed in Gaza, according to the territory’s Hamas-run health ministry.