Nearly two-thirds, 62 percent, 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 June 2 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 June 19th, 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.
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 percent would prefer to have a monarchy with Felipe as king while 36 percent would support a republic.
Republican sentiment remains strong in Spain, which only restored the monarchy in 1975 after the death of General Francisco Franco.
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 mostly 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 June 4th and 5 th