“Those in positions of influence must do all they can to lead people on a path away from violence,” Beattie, who was elected UUP leader this week, told the News Letter newspaper.
His call for calm came after a member of the Loyalist Communities Council (LCC), which has historic ties to unionist paramilitaries, warned on Wednesday that violence should not be considered “off the table”.
LCC member Joel Keys told UK lawmakers: “It worries me that we could potentially reach a point in this country … where the people feel that they do have to defend themselves.”
The post-Brexit “protocol” came into effect at the start of 2021, keeping Northern Ireland in the EU single market and customs union, despite the UK’s departure from the bloc.
Unionists believe it has created an “Irish Sea border” between Northern Ireland and mainland Britain — England, Scotland and Wales — threatening its status as part of the UK.
They also say it increases the prospect of union with neighbouring Ireland.
Northern Ireland is still deeply divided between pro-UK mainly Protestant unionists and pro-Ireland largely Catholic nationalists, despite a 1998 peace deal that ended three decades of violence over British rule.
Beattie said UK Prime Minister Boris Johnson “must engage with political parties… to meet to discuss our alternatives to the Northern Ireland protocol”.
“We must show that politics can provide solutions rather than dismiss the genuine concerns of unionists and the loyalist community,” he added.
UK Northern Ireland Secretary Brandon Lewis and Brexit minister David Frost both met LCC leaders on a visit to Belfast last week.
Frost on Monday urged the EU to compromise over the protocol before Northern Ireland enters a tense summer of events marking the Protestant ascendancy over Catholics.