La Palma's Cumbre Vieja volcano erupted this week, prompting the evacuation of 6,000 residents. It is located in the Canary Islands. Dozens of properties, mostly private homes, have since been destroyed by the resulting lava flows.
La Palma airport, where King Felipe and Queen Letizia had been due to arrive on Thursday, is now threatened by an ash cloud.
Spanish publication El Diario reports the airport could be closed, as the cloud is blown in from the west.
Airline Binter has warned passengers flights to the island could be cancelled.
Video from the island showed villas and swimming pools swallowed by lava.
There are no reports of casualties due to the prompt evacuation plan by authorities.
King Felipe and Queen Letizia were due to be accompanied by Pedro Sánchez, the Spanish prime minister, who was to fly in from New York after addressing the UN General Assembly.
During the initial Cumbre Vieja eruption lava flows up to 12 metres high were reported.
Magma is continuing to ooze from the volcano, and this is expected to continue for some weeks.
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The Canary Islands, a Spanish territory off the coast of Morocco, has a long history of volcanic activity.
The longest recorded eruption on La Palma took place in 1585, lasting 84 days.
In 1971, there was an eruption lasting 25 days - the shortest recorded on the island.
Authorities are warning toxic gas clouds could be created if the lava manages to reach the sea.
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During the Teneguia volcano eruption, in 1971, one person was killed by toxic gas.
This was despite lava largely avoiding populated areas.
Speaking to El Pais, Raúl Pérez, from the Geological and Mining Institute of Spain, said the eruption appears to becoming less intense.
He said: “The earthquakes that came with it are telling us that the magma keeps searching for new paths to the surface, but with the same eruptive style: the lava flows down the hillside without explosive eruptions.
“In theory, any volcanologist will tell you that no two eruptions are the same and that each has its own peculiarities.
“However, we are finding characteristics that are quite convergent with historical events in the Cumbre Vieja area: the lava flows favour the back flank and the magma takes advantage of the fractured terrain to find an easier way out.
“This, in a way, can help make the explosions less violent.”
Even after the eruption finishes, it will be some time before residents can return to their homes while authorities measure toxic gas levels.
Ana Crespo Blanc, a geodynamics professor at Granada University, said she expects the lava to meet the sea.
She said: “The most likely scenario is an accumulation of lava that will reach the sea, where it will cool down and perhaps even increase the size of the island.”