Speaking at a dinner banquet at Algiers in honour of visiting Pakistani President Pervez Musharraf on Wednesday night, Bouteflika said the dispute, currently being discussed at the United Nations Security Council, "has lasted too long".
Bouteflika asked his guest, who was travelling to Morocco on Thursday on the last stop of a three-nation Maghreb tour, to carry "a message of friendship to...our brothers in Morocco".
"We are ready to give relations between the two countries a new start, leaving aside some issues to be decided by the United Nations," he said.
Morocco's reaction to Bouteflika's remarks was mixed. Government spokesman Nabil Benabdellah said Morocco had always expressed "a willingness to establish normal ties" with Algeria.
But he added, "We want a concrete stand and clear faith in order to have a significant strengthening of our ties." He did not elaborate.
Benabdellah said Morocco could not accept the latest UN plan to solve the long-running dispute over the sparsely populated Western Sahara, which is also said to have offshore oil deposits.
"We are ready to give relations between the two countries a new start".
The plan, presented by special UN envoy James Baker, would give the desert area immediate self-government until a referendum within five years when residents would choose between independence, integration with Morocco and semi-autonomy.
Both the Polisario and Algeria have accepted the plan. "The proposal under its current form does not suit Morocco...We can't support a plan that might lead us to give up a part of Moroccan territory," Benabdellah said.
Although the land border between Algeria and Morocco has been closed since 1994, bilateral contacts have intensified in recent months, including on the fight against Islamic groups in both countries.
A possible rapprochement between Algiers and Rabat is being watched closely by European Union governments, keen to have political stability and economic growth on the southern Mediterranean shore.
Morocco seized the vast, mineral rich Spanish colony of Western Sahara in 1975 and Algeria backed the Polisario Front independence movement, which fought a low-intensity guerrilla war with Rabat for 15 years until a ceasefire in 1991.