Italy's populist interior minister Matteo Salvini has previously demanded other European Union nationals take migrants before allowing vessels access to Italian ports, and even required such an agreement before letting migrants picked up by an Italian coastguard vessel disembark.
The migrants have been stranded on the Spanish charity ship Open Arms since it picked them up off Libya in early August, and Rome's far-right interior minister, Matteo Salvini, refused to allow them to disembark.
"Once again, my European counterparts are offering us a helping hand", Conte wrote, while slamming Salvini for "dishonest collaboration".
"I understand your faithful and obsessive concentration on addressing the issue of immigration by reducing it to the formula of "closed ports". I am a minister to defend the borders, the security, the honour, the dignity of my country".
The squabbling between Mr Salvini, who leads the anti-migrant League, the populist government's junior partner, and Ms Trenta, who is from senior coalition party the 5-Star Movement, reflects exploding political tensions that have put Premier Giuseppe Conte's 14-month government on the verge of collapse.
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Both M5S and PD on Tuesday voted against Salvini despite his last-minute offer to back a plan to slash the number of the country's lawmakers.
"We're waiting", the Open Arms spokeswoman said.
Even as the fighting over the Open Arms boat played out, another migrant rescue boat drama loomed.
On Wednesday, as storms were heading towards the boat's position, a court in Rome ruled that Salvini's so-called "security decree" against the vessel was in violation of global laws.
5-Star and the opposition Democratic Party (PD) have stalled any debate of the League's no-confidence motion and many of their politicians are now openly discussing forming a coalition among themselves to sideline Salvini.
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Trenta said she acted "listening to my conscience".
She added: "We can't forget that behind the polemics of these days there are children and youths who suffered violence and every kind of abuse". Salvini says he will continue to deny the ship entry into Italian waters, despite the court's ruling.
He added: "Humanity would be investing seriously in Africa, certainly not opening Italian ports".
Since coming to power in June 2018, Salvini has repeatedly taken a hard line against migrants.
"Portugal, Spain, France, Germany and Luxembourg are the countries that have expressed their willingness to welcome the group of people, in a gesture of humanitarian solidarity and a common desire to provide European solutions to the issue of migration and human tragedies in the Mediterranean", Portuguese Ministry of Internal Administration announced in a statement.
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Another rescue ship the Ocean Viking, operated by SOS Mediterranee and Doctors without Borders (MSF), which is also looking for a port to dock with more than 350 migrants on board, was on Thursday also near the coasts of Lampedusa and Malta.