The majority of Spaniards want a referendum on the future of the monarchy, according to a poll published less than a week after King Juan Carlos abdicated in favour of his son.

Nearly two-thirds – 62% – believe a referendum should be held "at some point" to decide whether Spain should continue to have a monarchy, the survey in centre-left daily newspaper El Pais showed.

Within hours of the 76-year-old king's announcement on 2 June that he was abdicating in favour of his son, thousands of people massed in central Madrid and other cities to demand a referendum on the monarchy.

Thousands took to the streets again on Saturday, calling for a popular vote on the issue.

Crown Prince Felipe, 46, is due to be crowned, probably on 19 June, in a joint session of parliament – whose members, both in the ruling party and in opposition, overwhelmingly support the monarchy.

But a spate of scandals over the past three years has caused a dramatic drop in the monarchy's popularity, while public faith in Spain's institutions in general has declined during the economic crisis gripping the country.

If a referendum were to be held, the poll found 49% of people would prefer to have a monarchy with Felipe as king while 36% would support a republic.

Republican sentiment remains strong in Spain, which only restored the monarchy in 1975 after the death of General Franco.

The prime minister, Mariano Rajoy, has rejected calls for a referendum on the monarchy. He argues that Spain's 1978 constitution, which established a parliamentary democracy with the king as a largely ceremonial head of state, was supported by a great majority in a referendum at the time.

The El Pais survey of 1,000 people was carried out by the Metroscopia polling firm on 4-5 June.