The Stormont executive has issued a joint call for threats against workers conducting Brexit port checks to be "lifted immediately".
Physical inspections at ports in Larne and Belfast were suspended by Stormont's agriculture department on Monday after Mid and East Antrim Council (MEABC) withdrew staff over security fears.
EU officials in Northern Ireland have also been temporarily withdrawn from their duties at the ports.
It follows graffiti opposing Irish Sea border checks being daubed in some loyalist areas in recent days, with port staff referred to as "targets".
Port staff have also reported suspicious activity, including apparent attempts to record vehicle number plates.
There is no indication at this stage whether the threats are from loyalist paramilitaries.
Police stepped up patrols and are expected to hold discussions with Mid and East Antrim council and officials from the Department of Agriculture, Environment and Rural Affairs (Daera).
Lorries arriving at new inspection facilities at Belfast Port this morning were turned around and redirected by UK Border Force officials.
Stormont parties have been sharply divided on the Northern Ireland Protocol as part of the UK-EU withdrawal agreement since it came into effect in January.
It is aimed at keeping the land border between Northern Ireland and the Irish Republic open, but it imposes controls on trade from Britain to Northern Ireland.
In a joint statement from the five-party Northern Ireland Executive, ministers called for the threats to be lifted.
They said: "As public servants, these staff should be allowed to do their jobs without fear and it is unacceptable and intolerable that threats have been made.
"The threats should be lifted immediately and staff should be allowed to return to their posts and get back to their work.
"There is no place in society for intimidation and threats against anyone going to their place of work."
Twelve MEABC staff at Larne Port were withdrawn from their duties on Monday. The council said this followed an "upsurge in sinister and menacing behaviour in recent weeks".
The council's mayor, DUP councillor Peter Johnston, did not wish to speculate on the source of the reported threats to staff but told Belfast Live they were "credible".
He told Belfast Live: "When we were given the information yesterday, it was on the basis that we knew there were threats, we knew they were credible threats, and it was compounded tension over the past weeks that has led up to this.
"It's the job now for the PSNI to get working on that, to investigate and to make sure that we remove and mitigate any risk to our staff.
"We won't be allowing our staff to return - I certainly wouldn't want to oversee it - until those risk assessments come back from the PSNI, from Daera, from the Food Standards Agency and from the council, that say they're safe to do so."
Outgoing DUP Agriculture Minister Edwin Poots told BBC Radio 4's Today programme said it is "difficult" for politicians to control anger within the unionist community over "disproportionate" Irish Sea regulatory checks.
Taoiseach Micheál Martin told RTE the ports safety concern is a "very sinister and ugly development".
"Obviously, we will be doing everything we possibly can to assist and to defuse the situation," he added.
Police last month warned discontent in loyalist communities was "growing" over the NI Protocol.
Assistant Chief Constable Mark McEwan told MPs graffiti and online monitoring provided early pointers of the discontent, but feedback was not causing police significant concern.
Unionists have urged the UK government to scrap the Protocol over concerns about disruption to trade from Britain to Northern Ireland.
Nationalists do not support the disruption but say the Protocol is necessary to prevent a hard land border with the Irish Republic.
Focus on the Protocol intensified last Friday after the EU threatened to trigger Article 16 to suspend aspects of its operation in a dispute over coronavirus vaccine supplies in the bloc. The European Commission swiftly backtracked after facing intense criticism.
