Spanish foreign minister Alfonso Dastis has said his government had been “surprised by the tone of comments coming out of Britain” about Gibraltar.
He told a Madrid conference: “It seems someone is losing their cool.”
On Sunday ex-Conservative leader Lord Howard said the UK would be willing to defend Gibraltar in the same way it defended the Falklands 35 years ago.
And Gibraltar’s chief minister Fabian Picardo said: “Gibraltar is not a bargaining chip in these negotiations.”
“Gibraltar belongs to the Gibraltarians and we want to stay British.”
The current row was sparked by draft Brexit negotiating guidelines published by the EU last Friday saying any decisions affecting Gibraltar would be run past Spain.
The guidelines said: “After the United Kingdom leaves the Union, no agreement between the EU and the United Kingdom may apply to the territory of Gibraltar without the agreement between the Kingdom of Spain and the United Kingdom.”
There was a similar message from UK Foreign Secretary Boris Johnson as he arrived at EU foreign ministers’ meeting in Luxembourg.
Mr Johnson said: “The sovereignty of Gibraltar is unchanged and is not going to change, and cannot conceivably change without the express support and consent of the people of Gibraltar and the United Kingdom, and that is not going to change.”
Theresa May has said the UK is “committed” to the territory and its sovereignty is not on the table during Brexit talks.