Anti-immigration leader Mr Salvini aimed a dig at Emmanuel Macron and his officials after Italy was accused by the French interior minister Christophe Castaner, of refusing to discuss alternative immigration policies.
The warning did not go down well with the Italian populist leader, who told France to refrain from lecturing his country.
Saying that Italy’s patience was running thin, Mr Salvini, leader of the anti-immigration party Lega, wrote on Twitter: “The French interior minister accuses me of ‘systematic refusal to every type of opening’.
“Are these the lessons from Macron and his friends who ‘unload’ migrants in Italian forests at night? No thanks.”
Mr Salvini’s angry message comes after French police officers were caught “dumping” illegal immigrants in Italy.
Members of the French border patrol were caught on camera earlier this month driving across the border and releasing three immigrants without notifying local authorities, an act the French government said last week was an “error”.
Pictures and video of the astonishing event were released on social media by Mr Salvini himself, leading to the escalation of tensions between Rome and Paris.
The interior minister has since increased police presence at the border with France, focusing patrols’ attention on Claviere, the Italian alpine town where the migrants were released.
In a separate message, Mr Salvini said: “Italy is no longer fearful, resigned to being the refugee camp of Europe and to taking orders from Brussels and Berlin.”
He then invited Mr Castaner to meet him in Rome to talk through their border issues.
He said: “I’m waiting for the French minister in Rome, but in the meantime we will continue to patrol the borders.
“We are a country that has lifted its head up again: those who have not yet understood that should realise it.”
Mr Castaner said on Sunday he had no interest in intensifying the debate and looked forward to discussing the migrant issue with his European counterparts, including Mr Salvini.
He said: “I think the solution is found in co-operation, never in opposition.
“Unilateral decisions won’t make us achieve anything.
“Today, Italian and French border patrol forces work well together in the majority of bordering areas.
“Don’t count on me to fuel the controversy.
“The most important thing now is for the police of our countries to meet to strengthen their collaboration.”
But Mr Salvini didn’t refrain from criticising even the French official’s latest remark, saying: “Happy to hear, Castaner is clearly criticising himself after French police officers dumped like package migrants in the Italian wood.
“Castanet has been recently appointed, I am sure we will work well together and with reciprocal respect.
“But we need facts, we are ready to carry on with our policies.”
Since his appointment as interior minister on June 1, Mr Salvini has promoted policies aiming at curbing the number of immigrants – banning NGO rescue vessels from disembarking in Italian docks and endorsing a move cutting off free school meals to children of immigrants.