Refugee 'hot potato'
Earlier this week, Rabat and Algiers traded accusations over allegations that the refugees were forced to make the crossing attempt.
On Friday, Morocco accused Algeria of expelling the Syrian group across the frontier near the desert town of Figuig, suggesting a deliberate attempt to embarasss Rabat.
Algeria subsequently responded by denying the refugees originated from Algeria.
Neither country has agreed to take in the group of Syrian refugees.
The two nations summoned each other's envoys in the latest row between the neighbours, who have kept their shared 1,500 km land border closed since 1994.
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'Sand War'
Since the 'Sand War' border disputes of the 1960s, Rabat and Algiers have shared a relationship fraught with tension, particularly over Western Sahara – a disputed former Spanish colony.
Morocco annexed the territory in 1975, however Algeria has supported and hosted the Polisario separatist group which is held in contempt by Rabat.
Dr. Abderrahim Esslimi, a Moroccan political analyst interviewed by The New Arab, accused Algeria of trying to deliberately "flood" Morocco with African and Syrian refugees to create tensions and destabilise its eastern neighbour.
But Saida Benhabiles, former minister of national solidarity and president of the Algerian Red Crescent told The New Arab the group of refugees are stranded on the Moroccan side, and not in the border region. In an angry tone she said: "We regret and strongly condemn the exploitation of this humanitarian tragedy for political purposes."
(Reporting by Hassan al-Ashraf, translation by Karim Traboulsi)
