The SVP has the backing of 26.1 percent of the people, according to the results released on Wednesday of a survey conducted by the gfs.bern institute.
That's down slightly from 26.2 percent in March but still well ahead of the Socialist party (19.3 percent, down from 19.6 percent), the second most popular party in the country.
The centre-right Liberals, meanwhile, showed the greatest growth in support at 17.1 percent (up from 16.3 percent), with their credentials backed by a belief that they are best placed to manage the Swiss economy.
Backing for the Liberals is two percentage points ahead of the support it received in the 2011 national elections.
Support for other centrist and left-wing parties dropped, with Christian Democrats at 11.5 percent (down from 11.8 percent), the Greens at 7.4 percent (down from 7.5 percent) and the Green Liberals at 4.8 percent (down from 5.6 percent).
The Conservative Democratic Party (BDP) fell to 4.4 percent from 4.6 percent, with media reports suggesting that federal cabinet minister Eveline Widmer-Schlumpf, a member of the party, faces a challenge getting re-elected.
The BDP was initially formed by disgruntled SVP members from the cantons of Graubünden and Bern.
Widmer-Schlumpf joined the fledgling party after being expelled from the SVP when she accepted an election to the federal cabinet in 2007 that was not supported by the SVP.
She subsequently went on to serve as president in 2012.
The Swiss People's Party, with its nationalist policies and support for immigration restrictions, remains popular at a time when the issue of immigration and asylum seekers is the biggest concern of voters, according to another survey by gfs.bern.
The survey results, released by state broadcaster SSR on Wednesday night, showed the issue is the top concern of 34 percent of Swiss.
This ranks well ahead of relations with the European Union (10 percent) and the environment (five percent).
The SVP is identified as the party with the best competence to deal with asylum seekers and immigration.
“We identified this problem before the others and the citizens know it,” Claude-Alain Voiblet, SVP vice-president told the Tribune de Genève newspaper.
The SVP spearheaded a popular initiative, approved in a national vote in February 2014, to cap immigration from the European Union.