Foreign Minister Arancha Gonzalez Laya was moving to allay fears after some countries reimposed travel restrictions on Spain.
"Spain is a safe country," she told reporters. "Like other European countries, Spain has new outbreaks. It's not unusual."
Madrid is making "great efforts to control these outbreaks", she said after Spain reported nearly 1,000 new cases on both Thursday and Friday.
As well as killing more than 28,000 people, the coronavirus has dealt a major blow to Spain's tourism industry, which normally accounts for 12 percent of GDP.
The number of COVID-19 cases has tripled in two weeks, and the authorities are monitoring more than 280 outbreaks.
Passengers arriving from Spain to the UK must now spend a fortnight in isolation. Norway has reimposed quarantine on travellers from Spain.
And French Prime Minister Jean Castex "strongly recommended" Friday that the French avoid going to Catalonia, a region in northeastern Spain where the epidemic is particularly on the rise.
Earlier Sunday, a spokesman for the Spanish foreign ministry told AFP that the new outbreaks had been "located, isolated and controlled".
Madrid was "in contact" with London whose decisions it "respects", he added.
Spain suggests islands exemption
Gonzalez Laya said one possibility was to exempt Britons from the quarantine if they were returning from the Balearic or Canary islands, where cases has been limited.
The British government defended the quarantine requirement, which took effect at midnight on Saturday, just hours after it was announced.
"The data... showed a big jump right across mainland Spain," Foreign Secretary Dominic Raab told Sky News. "We can't make apologies for doing so," he said, adding: "We must be able to take swift, decisive action."
Among Britons affected by the decision is Transport Secretary Grant Shapps, currently holidaying in Spain.
The health ministry is particularly concerned about the situation in Aragon and Catalonia, where the regional authorities have urged residents of Barcelona to stay at home.
They also decided on Friday to close nightclubs and bars, considered hotbeds of contagion.
Most regions have tightened the screws by reinforcing the compulsory use of masks, which must be worn at all times in the street under threat of a fine.
Some of them are limiting the number of people who can meet or banning visits to retirement homes.
But the central government insists that this is not a "second wave".
It has ruled out the possibility of a new state of emergency, like the one earlier this year, when Madrid imposed a strict lockdown in mid-March that was not completely lifted until June 21.
Spain, one of the countries most affected by the pandemic, has reported 272,400 cases and more than 28,400 deaths.