"As an act of good faith ... I will propose that parliament introduces a change in the law so that the 59 boats can fish again based on their historical fishing practices," Gibraltar Chief Minister Fabian Picardo told Spanish newspaper El Mundo in an interview published on Friday.
The quote was backed up by a spokesman for the Gibraltar government.
The dispute broke out last month after Gibraltar's construction of an artificial reef using concrete blocks in the bay off the tiny territory. Gibraltarian authorities say the move was necessary to help marine life recover from overfishing.
Commission fact-finders set to visit rock in September
Picardo said Gibraltar would not remove the concrete blocks, and rejected four-way talks with Spain, Britain and Andalusia, which is one of Madrid's proposals to end the standoff. But the indication that that the outcrop is prepared to relent on the Spanish fishing fleet increases the prospect of a settlement of the dispute.
Earlier this week Spain's foreign minister, José Manuel García-Margallo, said that the border checks would continue until Spain regained confidence in Gibraltar's government.
While Spain has threatened to take its claim on Gibraltar to the United Nations, Britain last week called on the European Commission, the EU's executive, to send in monitors to check whether Spain's controls breach EU rules.
Spain lays claim to the territory, with a population of just 30,000, which it ceded to Britain by treaty 300 years ago.
As well as tightening border controls, Spain has threatened to charge tourists a €50 border levy, restrict the use of Spanish air space or block Gibraltar's lucrative ship fuelling industry.
The European Commission is set to send a fact-finding mission to Gibraltar in September to examine the legitimacy of border controls imposed by Spain during the dispute.