The Foreign Office lodged a formal complaint with Spain after a British diplomatic bag was opened by a Spanish border guard.
Gibraltar's chief minister is to meet David Cameron amid allegations that Spanish border police have come under attack from angry motorists.
Pictures posted on Twitter show Spanish divers hanging flags over the controversial boulders.
The packages that were opened on Gibraltar's border with Spain were not diplomatic bags, Spain's Foreign Minister said.
Jose Garcia-Margallo reportedly told the BBC: "There is no incident. If it is not a diplomatic bag, there is no diplomatic incident. A bag was opened, which was not a diplomatic bag."
A Foreign Office spokesman said the bags were "clearly marked as the property of HM Government" and, as such, were covered by the Vienna Convention.
British warships should be sent to Gibraltar to show the UK's determination to defend the region, Conservative MPs urged today.
Already tense relations between Spain and the UK were heightened earlier this week after a diplomatic bag was opened by a Spanish border guard on the border.
Peter Bone said Royal Navy ships should make a "goodwill visit" to the territory to build trust with the Gibraltarians, before adding he would prefer to send a couple of gunboats instead.
Fellow Tory and former minister Bob Neill went on to ask the Government to consider reinforcing the UK's naval deployments available in Gibraltar.
Former army colonel and now Tory MP Bob Stewart suggested last week that Britain should send major combat units to train in Gibraltar to show its determination to defend the region.
Spain has given an assurance there will be no repeat of the incident in which officials on the border with Gibraltar searched a British diplomatic bag, the Foreign Office has said.
The incident, which took place on Friday, was described by a Foreign Office spokesman as a "serious infringement" of international diplomatic protocols.
– David Lidington, Minister for Europe
In our protests we requested an urgent explanation of this incident from the Spanish Government and sought assurances that there will be no further interference with the UK’s official correspondence.
We have now received that explanation from the Spanish and have been assured that we will not see a repeat of these actions.
The British Government should increase the Royal Navy's presence in Gibraltar in response to Spanish incursions into its territorial waters, Chief Minister Fabian Picardo has said.
Mr Picardo said the latest alleged incursion - a Spanish research vessel ignoring requests to leave the territory's waters for 20 hours - was a "security issue that Spain needs to be aware of".
He told BBC Radio 4's Today programme that he was "in favour of anything that has a positive deterrent effect" but that "diplomatic aspects must be equally important".
The Foreign Office has accused a Spanish survey ship of acting unlawfully and provocatively by sailing into British waters around Gibraltar.
This evening it responded by summoning the Spanish Ambassador - for the third time in two years - to explain the alleged incursion.
ITV News Europe Correspondent Emma Murphy reports:
A spokesman for the Ministry of Defence (MoD) has said that the Royal Navy took "proportionate responses" after a Spanish vessel allegedly entered British waters off the coast of Gibraltar:
The Ramon Margalef, a Spanish State oceanographic survey ship, entered British Gibraltar Territorial Waters on the evening of Monday 18 November and unlawfully conducted survey operations for 22 hours in violation of United Nations Convention on Law of the Sea (UNCLOS).
The RN Gibraltar Squadron's Fast Patrol Boats HMS Sabre and HMS Scimitar, in accordance with UNCLOS, challenged the Ramon Margalef's presence by issuing appropriate warnings and preventing the deployment of the Ramon Margalef's oceanographic surveying probe.
– MoD spokesman
There was no damage to any Royal Navy or Spanish equipment or vessels and no injuries were incurred.
The actions of the Royal Navy were fully in accordance with Her Majesty's Government's commitment to uphold the sovereignty of Gibraltar with a range of proportionate responses.
This is the third time the Spanish Ambassador has been publicly summoned in relation to Gibraltar since the current Spanish government took office in December 2011.
An MP raised the issue of the alleged incursion by a Spanish vessel into British waters in a Westminster Hall debate earlier today, describing it as "a very serious incident".
Labour MP Jim Dobbin asked: "Is a minister from the Foreign Office coming to make a statement on what is a very, very serious incident?"
Deputy Speaker Lindsay Hoyle replied: "I've been given no notification of a statement to be made but I'm sure the Foreign Office is listening very carefully to what you've just said on such a serious incident."
This video is believed to show a Spanish vessel - the RV Ramon Margalef - in British waters off the coast of Gibraltar.
It was uploaded to YouTube yesterday and purportedly includes extracts of the radio conversation between the ship's skipper and Gibraltar authorities.
ITV News cannot independently confirm the veracity of this footage.