"Our objective is the disembarkation in a port of safety of the 629 people now on board the Aquarius - some we rescued yesterday night in hard conditions", she was quoted by Reuters as saying.
The rescue service says its patrol craft intercepted six different boats carrying migrants that had left from African shores throughout Saturday.
"We comply with global commitments regarding humanitarian emergencies", Sánchez wrote on Twitter. Asylum seekers leaving Africa and the Middle East typically set off in rubber vessels that have little chance of making it across the Mediterranean. Malta, which in the last few years has only accepted a few hundred migrants, refused, retorting that it bore no responsibility because Italy had co-ordinated the rescues in Libya's search-and-rescue zone.
The episode has divided opinions in southern Italy, with anti-migrant moods apparently on the rise.
The Aquarius, a rescue vessel operated by aid organizations Doctors Without Borders (also known as Médecins Sans Frontières) and SOS Mediterranée, was forced to wait in the Mediterranean Sea between Italy and Malta after failing to receive guidance from Italian authorities.
Italy has always been a destination for migrants crossing the Mediterranean and has been dealing with a surge in arrivals in recent years. Since the start of the year, almost 14,000 migrants have arrived in Italy; an additional 500 have died attempting the journey. They need to go to the port that is safest and closest.
Spanish journalists on board the rescue vessel have reported the increasingly desperate plight of the migrants over the past 24 hours.
"Saving lives is a duty, turning Italy into a huge refugee camp is not".
SOS Mediterranee tweeted late on Sunday that the Aquarius had "received instructions from the Italian Maritime Rescue Coordination Centre to standby in our current position which is 35 nautical miles from #Italy and 27 nautical miles from #Malta".
Italian Premier Giuseppe Conte said on Facebook that he had called on his Maltese counterpart, Joseph Muscat, to "explicitly at least take on the human assistance of persons in difficulty aboard the Aquarius".
"The NGOs have said the time to get to Valencia would be too long given the humanitarian situation on board".
Another local resident, Natale Lombardo, said illegal migrants disembarking on the island were virtually "invading" them, adding that "he who arrives here legally is welcomed, but between these people there are also illegals and those can't be tolerated".
"This shows what happens when there are not enough rescue assets at sea", Sea Watch spokesman Ruben Neugebauer said. "And then more people will die".
At a news conference Monday afternoon, Salvini was asked whether Spain's humanitarian gesture was a "slap in the face" to Italy.
"I wish I had tens of slaps like these", Salvini said.