Joseph Garcia, deputy chief minister of Gibraltar, said failure to do so would put thousands of jobs at risk.
He pointed out that Brexit is casting uncertainty for communities throughout the UK and Europe that will be affected by changes in trade, freedom of movement and job prospects.
But few have as much directly at stake as the Gibraltarians, over nine out of 10 of whom voted last year in favour of staying in the EU out of fear that they could be left at the mercy of Spanish designs to impose its sovereignty on The Rock.
Along with Northern Ireland, Gibraltar is one of the few places where Britain shares a land border with another EU state, complicating the divorce proceedings which have recently got underway in Brussels.
Garcia said Brexit could affect about 12,000 workers who cross the border into Gibraltar daily. Over 50 per cent of them are Spaniards.
Speaking during a visit to the European Parliament, Garcia said it was essential to both Gibraltar and the adjoining Spanish region that a free flowing border is maintained for residents, frontier workers and tourists.
"Bearing in mind both the result of the EU referendum in Gibraltar and Gibraltar's unique status under EU law, Gibraltar maintains that it should be possible for Gibraltar to have continued access to the single market in services."
He said the relationship between Gibraltar and Spain is a "textbook example" of two separate parts of the EU "coming together to create jobs and mutual prosperity."
The visit to Parliament sought to highlight the case of Gibraltar where 96 per cent voted in favour of the Remain side.
He warned, "Jobs occupied by frontier workers represent 40 per cent of the total number of jobs in Gibraltar. While about 60 per cent of workers are Spanish, the remaining 40 per cent is composed of EU citizens from almost every member state.
"A frontier which lacks the necessary fluidity for people to be able to access their places of work directly puts at risk the jobs of over 12,000 EU citizens who live in Spain and work in Gibraltar."
Graham Watson, a former MEP for the south west of England, which includes Gibraltar, also accompanied Garcia on the visit to Brussels.
He pointed out that Brexit has brought uncertainty which many fear is likely to last throughout the two years of negotiations.
In April, the UK Foreign Secretary Boris Johnson moved to allay such fears when he said, "The position of the government is very, very clear, which is that the sovereignty of Gibraltar is unchanged and it is not going to change and cannot conceivably change without the express support and consent of the people of the Gibraltar and the United Kingdom."
On 13 June, the European Court of Justice (ECJ) ruled that trade between the UK and Gibraltar cannot be treated in the same way as trade between separate EU member states.
In a ruling that could have practical consequences for Spain's demand of a right of veto over Brexit trade arrangements insofar as they apply to Gibraltar, the ECJ upheld Gibraltar's separate and distinct status within the EU, but said, "It follows that the provision of services by operators established in Gibraltar to persons established in the United Kingdom constitutes, under EU law, a situation confined in all respects within a single member state."