The migrants, including pregnant women and scores of children, were saved by the French charity SOS Mediterranee on Saturday.
They were taken on board its ship Aquarius, which is now between Malta and Sicily. Malta and the new populist government in Italy each refused to take the migrants in, accusing one another of failing to meet their obligations.
The row has triggered international concern about the migrants' plight.
"It is our obligation to help to avoid a humanitarian catastrophe and to offer a safe port to these people," his office said in a statement.
SOS Mediterranee director general Sophie Beau said Spain's offer "is encouraging and shows that some states are sensitive to the humanitarian emergency." She warned that the ship will have to travel some 1,300 kilometres (800 miles) to reach the Spanish coast and that by tomorrow "there will be no more food (on board) apart from energy biscuits."
Malta's Prime Minister Joseph Muscat said in a tweet that "Malta is going to send fresh supplies to the ship." Italy and Malta thanked Spain for stepping up, but maintained their dispute over who was responsible.
Muscat tweeted his thanks to Sanchez "for agreeing to accept the Aquarius after Italy violated international law and caused an impasse." He added: "It will be necessary to sit down and discuss how to prevent this kind of thing from happening in the future. This is a European issue."
Beau said that under maritime law the ship should be allowed to dock in one of the nearest countries, Italy or Malta.
The UN had called on Malta and Italy to immediately allow the boat to dock, describing the situation as "an urgent humanitarian imperative".
The EU and the bloc's biggest member state Germany made similar pleas. "The priority of both the Italian and Maltese authorities should be ensuring these people receive the care they need," European Commission spokesman Margaritis Schinas told reporters, calling for a "swift resolution".
Salvini refused to back down.
"Saving lives is a duty, turning Italy into a huge refugee camp is not. Italy is done bending over backwards and obeying, this time THERE IS SOMEONE WHO SAYS NO," he wrote on Twitter followed by the hashtag #closethedoors.
MSF Sea (Doctors Without Borders) said the medical situation of those on the Aquarius was "stable for now but unnecessary delay to disembarkation in safe port puts vulnerable patients at risk." "Particularly seven pregnant woman, 15 with serious chemical burns and several critical drowning hypothermia patients," MSF Sea said.
Conte said Sunday that Rome had sent two patrol ships with doctors on board "ready to intervene and ensure the health of anyone on board the Aquarius who might have the need".
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)