"We are hoping to find a speedy solution to this problem - one that is both humanitarian and well-organised," Leon said after his meeting with Vall.
The United Nations High Commissioner for Refugees urged Mauritania in an official statement on Thursday to allow the Asian and African migrants to disembark.
"At this point in time, the main priority should be to help these people and not let them drift on the high seas in precarious conditions," said George Okoth-Obbo, the agency's director for protection.
The boat left Guinea-Bissau for Spain but ran into mechanical trouble around February 2, before being intercepted by Spanish authorities.
Mauritania's government has argued that the migrants did not leave from Mauritania and so the country cannot take them in.
They also say they have little capacity to care for those aboard.
More than 30,000 people were caught trying to reach Spain's Canary Islands last year in a dangerous voyage that many undertake in search of a better life.
Most are African, but migrants from as far away as Bangladesh, India and Pakistan have also been intercepted by Spanish authorities.
The majority of the migrants on the boat are thought to be from Pakistan.