He told members of the Security Council on Monday that he had "concluded that there was no pressure on Morocco to abandon its claim of sovereignty over the territory and, therefore, that an independent Western Sahara was not a realistic proposition".
Van Walsum suggested breaking the impasse by basing further talks on two "realities" - that the Security Council would not force Morocco into a referendum but the UN would not recognise Rabat's sovereignty over Sahara without an accord.
Muhammad Khadad, a member of the Polisario Front leadership, described van Walsum's remarks as "ridiculous", and affirmed that the Polisario Front would continue UN-mediated negotiations with Morocco.
Divisions at UN
Van Walsum's comments sparked division in the Security Council between South Africa and some other non-aligned members [who believe that as an ex-colony Western Sahara should have a chance of independence] and the US, France and Spain, which have praised Morocco's autonomy plan.
Dumisani Kumalo, the South African ambassador to the UN and the current Security Council president, said there had been confusion in the council after van Walsum faxed his comments to its 15 members on Monday just before they were to consult on Sahara.
The council has to renew the mandate of a UN peacekeeping force there by April 30.
Kumalo said van Walsum's comments "seemed to contradict" a report on Western Sahara by Ban Ki-moon, the UN secretary-general, which was also before the council.
Ban's report does not take sides on the merits of the two plans.
Diplomats said a group of countries including the US was starting on Monday to draft a resolution to renew the mandate for some 230 UN peacekeepers in Western Sahara.
Morocco's seizure of Western Sahara prompted a guerrilla war for independence until a UN-brokered ceasefire in 1991.
Rabat has ruled out independence but offered autonomy for the that would enable the indigenous Sahrawi people to run their own affairs through various representative legislative, executive and judicial bodies under Moroccan sovereignty.
Polisario has urged a referendum with independence as one option.
Morocco and the pro-independence Polisario Front have held four rounds of talks with no substantial progress achieved, trading blame for the deadlock.
The UN-mediated talks last year brought together Morocco, the Polisario as well as representatives of neighbouring Algeria and Mauritania.
Morocco wants the talks to concentrate on the details of how to grant the region an autonomy.
The Polisario says the negotiation need to examine how to hold a referendum in which the Sahrawis would be offered a choice between independence, autonomy or integration into Morocco.