Algerian President Abdelaziz Bouteflika has met President George W Bush and his Secretary of State, Colin Powell, in Washington.
Energy co-operation and political and economic reform in Algeria were high on the agenda, but the discussions were also expected to cover United Nations proposals for the disputed territory of Western Sahara.
Since 1991, when a ceasefire ended the fighting in Western Sahara between Moroccan troops and guerrillas of the Polisario Front, the UN has been trying to get the two sides to agree on arrangements for a referendum to decide the future of the territory.
For the last four years, UN special envoy James Baker, a former US secretary of state, has been trying to break the deadlock over who should be allowed to vote.
Solution 'impossible'
Polisario maintains that the referendum should be limited to the 74,000 people counted in the census of 1974, when Western Sahara was still a Spanish colony.
Morocco says many more are entitled to take part, including more recent arrivals.
Neither side will give way, since both believe the size and make-up of the electorate will determine whether the territory is ruled by Morocco or becomes independent.
Mr Baker has now concluded that reaching agreement is virtually impossible.
The UN Secretary-General, Kofi Annan, endorsed that view in a report to the Security Council at the end of June.
Alternative autonomy plan
The Security Council, in turn, urged the parties to discuss an alternative: Mr Baker's autonomy plan.
This came as a bombshell to Polisario and its backers.
Although Western Sahara would have internal self-government, with responsibility for the key sectors of phosphate mining and fishing, Morocco would control national security as well as foreign affairs and defence, including everything relating to weapons and explosives.
Most controversially, there would be a referendum on the status of the territory within five years, and everyone having lived there for at least a year would be entitled to vote.
That could include large numbers of settlers from elsewhere in Morocco.
'Plan deprives Sahrawi'
The reaction from Algeria came in a memorandum from Mr Bouteflika to Mr Annan only recently made public.
The Algerian president says such a referendum would be open to every kind of manipulation and deprive the Sahrawi people of their right to self-determination.
In general, he says, the draft plan favours only one approach: the integration of Western Sahara into Morocco.
It confirms the illegal occupation of the territory in violation of previous UN resolutions.
The new approach certainly amounts to a drastic about-turn.
The big powers are tired of the deadlock, and if no agreement is possible on autonomy they are likely to walk away from the problem altogether.
The Moroccans would have the most to gain from that.