"Obviously we will have to extend this situation...in 15 days I do not think that we will be in a position to win this battle," Transport Minister Jose Luis Abalos told RNE radio.
Spain is suffering Europe's second-worst outbreak after Italy.
Its 47 million people have been under partial lockdown since Saturday night as the country tries to stem the coronavirus outbreak. People are only allowed to leave their home to go work, to the pharmacy or a hospital.
The government has taken widespread measures including using drones to send public messages telling people to go home, but it has not closed its borders so far, with tourism suspended at its border with Portugal but workers allowed through.
Abalos said it remained to be seen which measures would be prolonged.
Meanwhile, Interior Minister Fernando Grande-Marlaska told Cadena Ser radio that closing Spain's borders was among the options under consideration.
Grande-Marlaska said he would discuss the potential border closure alongside other measures with fellow EU ministers today.
Asked if closing Spain's borders was a possibility, he said: "It's a possibility, of course, it's a real option to fight against the spread of the virus."
Over the weekend, several countries worldwide imposed bans on mass gathering, shuttered sporting, cultural and religious events, while medical experts urged people to practice "social distancing" to curb the spread.
Spain has the fifth-highest number of coronavirus cases in the world behind China, Italy, Iran and South Korea.
The government's official coronavirus death toll rose to 288 on Sunday, with 7,753 confirmed cases of infection.
Schools across the country are closed, keeping millions of children at home, while army specialists in protective suits spray disinfectant in train stations and a growing number of car plants close, either because of supply problems or coronavirus cases.
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