Greater Manchester Police said it arrested 16 people on suspicion of supporting a proscribed organisation, and that they remained in custody for questioning.
Police Scotland said officers in Edinburgh attended after the force was made aware of images online showing people holding placards in support of Palestine Action in Edinburgh’s Parliament Square area.
However, a spokesperson said no arrests were made as the protesters had gone by the time officers arrived. Enquiries are ongoing.
There were also no arrests at a separate pro-Palestinian protest in the city, the force added.
Separately, a march organised by the Palestine Coalition took place in London on Saturday.
The Met said 10 people had been arrested so far at that demonstration, including eight suspected of supporting Palestine Action.
Saturday’s protests came ahead of a High Court hearing on Monday at which the co-founder of Palestine Action, Huda Ammori, will ask for permission to challenge the decision to ban the group.
Last Saturday, 71 arrests were made across the UK at similar protests against the decision.
Palestine Action has engaged in activities that have predominantly targeted arms companies since the start of the current war in Gaza.
MPs voted to proscribe the group after activists broke into RAF Brize Norton in June, spraying two Voyager aircraft with red paint and causing £7m worth of damage. Palestine Action took responsibility for the incident at the time.
Four people have since been remanded in custody, charged with conspiracy to commit criminal damage and conspiracy to enter a prohibited place knowingly for a purpose prejudicial to the safety or interests of the UK.
The incident also prompted a security review across all UK military bases.
