Mr Picardo said he would support anything that would have a “deterrent effect” following the latest incident, which involved a Spanish research vessel ignoring requests to leave the territory’s waters for 20 hours.
Spain’s ambassador to the UK Federico Trillo was summoned to the Foreign Office and told that the incursions were “unlawful” and did not change international law or weaken the legal basis for British sovereignty.
Labour MP Jim Dobbin, chairman of the all-party parliamentary group on Gibraltar, has raised the prospect of shots being fired as the result of a misunderstanding between the British and Spanish.
Mr Picardo told BBC Radio 4’s Today programme: “I certainly hope we are not close to that at all and never will be.”
But he added: “It is a security issue that Spain needs to be aware of.”
Asked about the prospect of an increased military presence in Gibraltar, Mr Picardo said: “I would be in favour of anything that has a positive deterrent effect.
“I have discussed before the possibility of more senior assets of the Royal Navy being put at the disposal of the commander British Forces in Gibraltar.”
But he added that “diplomatic aspects must be equally important” and he had been working with Europe Minister David Lidington and Foreign Secretary William Hague on the issue.
“Calling in an ambassador, especially one that is an ambassador for a European Union partner and a Nato ally, is quite a dramatic step and Spain needs to realise that,” he said.
“In the full glare of publicity, this is not where they want to be.”