The families of eight people killed and secretly buried by the IRA are expected to seek a meeting with the chairmen of the Commission for the Location of Victims Remains later this week.
The commission last week called off two of the six searches and is due to make a decision tomorrow on whether to continue searching at the other sites. It is understood the searches may be called off but that the digging at Templetown Beach, near Carling ford, for the remains of Mrs Jean McConville will continue for some days.
Gardai at the site wish to excavate the remainder of the car park and part of an adjoining embankment because of the possibility of sand and earth movement at the site over the years.
Mrs McConville's eldest son, Robert, who was 17 years old and interned in Long Kesh when his mother was abducted and murdered, said yesterday his family had been in contact with the relatives of the other "disappeared" and they would seek a meeting with the Government-appointed commission to find out what was happening.
A spokesman for the commission said searching would continue at four sites today and tomorrow, when a decision would be made about whether to continue.
No further information was available, he said.
The McConville family have maintained a vigil at Templetown beach, some sleeping in a Portacabin on the site "out of respect for my mother's remains", Mr McConville said.
He added: "Each day we are hoping but that hope is slowly but surely running dry. If they were to find the remains of a body at some other site it would give us hope that the IRA is telling the truth."
Digging continued yesterday at Templetown beach; Tedavnet bog, Co Monaghan; Cullaville on the Louth/Armagh border; and Coghalstown, Co Meath.
The searches at Oristown Bog, near Kells, Co Meath, and at Lacken, Co Wicklow were called off on Friday after the commission decided, from information supplied by garda searchers, that there was no prospect of finding any remains on the basis of the information supplied by the IRA.