Switzerland has until February 2017 to implement a 2014 binding referendum demanding limits on the influx of foreigners to a country whose population is already a quarter foreign.
It is seeking to negotiate a compromise with Brussels, which has insisted it cannot brook any impediments to the free movement of people enshrined in bilateral accords. Talks have been on hold until the June 23 Brexit vote, Reuters reported.
In an interview with Swiss broadcaster SRF aired on Tuesday, Burkhalter said Bern had agreed with major EU countries to launch intense talks just after the Brexit vote with the goal of reaching a deal this summer that it could present to parliament.
Should Britain decide to leave, though, the EU could be preoccupied with the fallout of the momentous move, he added. "That would be a problem because if the EU makes this discussion a priority it is difficult for us to find a solution."
Implementing unilateral curbs on immigration could torpedo the series of bilateral economic accords between Switzerland and the bloc that include free movement and which stand or fall together.
The Swiss government estimates losing the accords could cut output by as much as 7 percent of gross domestic product by 2035. Business leaders have also said they would find it harder to get qualified staff.