"We want May 9 to be the end point," the Socialist politician said after the weekly Cabinet meeting in Madrid on Tuesday.
Sanchez also promised that by the end of August 33 million of the country's total population of around 47 million would have been vaccinated against Covid-19.
Three and a half times as many doses would be delivered in the second quarter as in the first three months of the year. "We will join all forces to relentlessly vaccinate and immunize. This is the main task of the government," the prime minister said.
By Tuesday, around 5.9 million people in Spain had received at least one vaccine dose, and 2.85 million people had already received their second.
Due to rapidly rising infection numbers, the parliament had approved a six-month state of emergency in the autumn at the request of the government.
Since then, a night-time curfew, among other things, has been in force in almost the entire country.
At the beginning of February, Spain was still one of the countries with the highest infection figures in Europe.
According to official figures, there were about 77 infections per 100,000 inhabitants within seven days.
In some Spanish holiday regions the situation is even better, with figures of around 26 on the Balearic islands and 16 in Valencia.