The Sea Watch 3 rescue boat carrying 257 migrants was allowed to dock in Sicily on Saturday.
The German charity announced that it docked at the port of Trapani, in western Sicily, and that before going ashore, all 257 people on board, including 70 minors, were tested for COVID-19.
Hours later, SOS Mediterranee announced that its Ocean Viking rescue boat with 549 migrants on board had been authorised to dock in Pozzallo, in southern Sicily, on Sunday.
It had warned on Twitter that it is "running out of some medication" and that "the health of 3 pregnant women is rapidly deteriorating."
The Italian coast guard took one migrant off the boat for medical reasons on Friday night, the fourth such evacuation from the Ocean Viking in recent days.
"Too often in the past 3 years those rescued at sea had to wait for days to disembark, to the detriment of their mental and physical health," SOS Méditerranée said.
"These inhuman stand-offs cannot become the norm. European countries urgently need to revive the process towards the predictable disembarkation mechanism," it added.
Earlier this week, Italy appealed to the European Union to press other member states to take some of the thousands of asylum-seekers who have arrived in the country in recent months, a sharp uptick since 2020.
But similar past appeals for EU solidarity largely went unheeded, and there was no immediate signal the Italian government’s latest pitch would prove more effective.
Italy's interior minister earlier in the week pressed the European Union for an “urgent” change of direction on migrant policy. Right-wing leader Matteo Salvini, whose anti-migrant League party is a member of the country's wide-ranging coalition, is insisting Premier Mario Draghi act decisively to stem the flow of migrants arriving on Italy's shores.