Updated at 6.30pm with Maltese government's statement
If the Maltese cannot cope with the obligations that come with the large rescue area it co-ordinates, then it should give up part of it, along with the fees it is paid, Italian Infrastructure Minister Danilo Toninelli said.
In a video clip uploaded on La Repubblica, the minister said that in the future, Malta would have to abide by the rule that migrants have to disembark in the nearest port.
He was being questioned by Italian media following the unpopular decision to close Italian ports to the NGO ship Aquarius, which is now en route to Valencia in Spain carrying several hundred migrants.
Toninelli said: "Malta receives a large amount of public money for the surveillance of its search and rescue area, even though this is in fact patrolled by Italian boats."
"If the Maltese are not up to the task, they just need to say so, modify the search and rescue area and we will take it - along with the funds."
But the Maltese government said in a statement later Mr Toninelli did not know what he was saying (see below).
The Maltese and Italian governments have often contested the "closest safest port" regulation. In the Aquarius case, the migrants were rescued closer to Lampedusa than Malta, which effectively means it was under Italy's responsibility.
This is the second time in one day that the tension between Malta and Italy over the Aquarius has flared up. Earlier, MPs from the Five Star Movement walked out of the Sicilian Assembly in protest when Maltese President Marie Louise Coleiro-Preca started to address the gathering.
Watch: Italian MPs walk out as President Coleiro-Preca addresses Sicilian assembly
You don't know what you are saying, Malta government tells Toninelli
In a statement issued this afternoon, the government said Mr Toninelli's statement had no legal and political basis and showed he was either misinformed or wanted to stir a useless controversy.
Malta, the government said, fulfilled its obligations and abided by all applicable conventions including its obligations within its Search and Rescue region. In the last years it invested millions in upgrading its equipment and had all the necessary means to coordinate all SAR events inside its area.
During the past years it never ignored a single case inside Maltese SRR.
Moreover, the government did not receive any funds for the control of its SAR area.
SAR was a service rendered by the state without payments. Any funds received were related to external border control under EU funds which had nothing to do with SAR. Italy, the government said, receives millions from this same fund.
"The minister’s statements may be interpreted as though this issue has nothing to do with migration but is rather a territorial issue. It is a baseless and frivolous attempt to try to impinge on the sovereignty of a neighbouring country," Malta said.