Mr Finucane was shot and killed by the loyalist paramilitary group the UFF in 1989.
He said people had worked hard within the loyalist communities to "keep a reign on things".
Mr Finucane was shot dead in his north Belfast home by the loyalist UFF in 1989.
The loyalist who founded the modern-day Ulster Volunteer Force has told BBC's Spotlight the group should disband.
The police said petrol and bottles were seized in the loyalist Glenbryn Parade area of north Belfast.
However it would be wrong to be too dismissive of the loyalist tantrum.
Members of the loyalist parties were due to meet on Thursday in a first step towards ending the dispute.
The other adjourned preliminary hearing due to begin on Thursday concerned the loyalist murder of Gerard Slane 24 years ago.
The widow of a prison officer murdered by the loyalist parmilitary Ulster Volunteer Force in 1993 has welcomed the news.
But Northern Ireland is entering the most tense period of the year - the climax of the loyalist marching season.
The shooting incident took place while a crowd was standing in the Hopewell Crescent area of the loyalist Shankill Road.
Meanwhile, police have praised those with influence in the loyalist and republican communities for helping avert trouble at Tuesday's Ballymena parade.
BBC: NEWS | UK | Northern Ireland | Church attack 'linked to parade'
He said a lot of these people were "kids" who had been very young when the loyalist paramilitaries called their ceasefires.
Richard Jameson is thought to have been shot by the Loyalist Volunteer Force, a dubious and late signatory to paramilitary ceasefires.
Even Sinn Fein, while complaining of double standards, does not want to see the loyalist parties thrown out of the talks.
The paramilitary splinter group, the Loyalist Volunteer Force (LVF), issued a statement denying the two men had any links to its organisation.
Mr Powell said the loyalist community had not got enough political support.
The Loyalist Volunteer Force was linked to the murder, but denied this.
On Saturday David Ervine of the loyalist Progressive Unionist Party said he believed the IRA was going to put its weapons beyond use.
Whether he can soothe the Greetin' Wean will depend both on Paul Murphy's child-minding skills and just how colicky the loyalist baby really is.
Mr Adams comments came following a statement by a loyalist lobby group, the Loyalist Commission blaming republicans for the collapse of the political institutions.
Meanwhile, around a dozen women from the loyalist Shankill Road area of Belfast staged a protest outside UUP headquarters where the meeting was being held.
Mr O'Hagan's killing was claimed by the Red Hand Defenders, a cover name used by both the Loyalist Volunteer Force (LVF) and Ulster Defence Association.
Ensuring that the loyalist parties participate in some fashion is important.
There have been 38 arrests in connection with the loyalist disorder.
When Mr Paisley accuses Mr Trimble of betraying Ulster, Mr Trimble will be able to point to the support of the loyalist parties for the plan.
Mr Finucane, a high-profile Catholic solicitor, was shot dead by the loyalist paramilitary Ulster Defence Association in front of his family at his Belfast home in 1989.
He was shot at a house in Summer Street in the loyalist Oldpark area of north Belfast on Wednesday night when his 12-month-old child and girlfriend were inside.
Mr Slane, a 27-year-old father of three, was shot dead by the loyalist Ulster Defence Association (UDA) at his home at Waterville Street, west Belfast, in September 1988.
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