"We will not make any concessions" in the battle for cabinet seats, said Toni Brunner, SVP chairman, even though his party's share of votes fell from 28.9 percent to 25.9 percent.
"We are still the biggest party as we were previously," he noted.
Since the 1950s, the seven ministerial posts have been allotted to the country's four biggest political parties -- two seats each for the centre-right Liberals, Christian Democrats and the Socialists, with the remaining seat going to the SVP.
That balance changed briefly when the SVP gained a second seat after their strong 2003 election showing.
However, one of the two SVP ministers was ousted from the party due to in-fighting, leaving it with effectively one cabinet seat again.
Even before the elections, the party had begun pushing to regain the cabinet post it lost when Justice Minister Eveline Widmer-Schlumpf broke away to form the BDP.
The SVP was returned as the biggest political party in Switzerland, although it ceded ground to the breakaway BDP, as well as the Green Liberals.
Most other major parties represented in the cabinet also saw a drop in support.
The Socialist Party obtained 18.1 percent, the Liberals 15.3 percent, while the Christian Democrats got 13.1 percent.
But all of these other key parties have said that they would not cede their cabinet seats.
Having obtained just 5.5 percent, the BDP should in theory return the cabinet seat to the SVP. But Widmer-Schlumpf has proven to be a popular minister, and a centre-left alliance may help to secure her place and isolate the SVP.
Christian Democrats said that the Liberals may have to give up one of their two cabinet positions if Widmer-Schlumpf is to keep her place.
"It can be tight for the Liberals," Jakob Buechler, a Liberal MP told Swiss newswire ATS.
A final decision on the shape of the government will be made in mid-December, after run-offs of some upper chamber seats are held.
But for Swiss daily Le Matin, "the time of change has begun."
"These federal elections 2011 marks a turning point in Switzerland's history," it said, noting the rise of new centrist parties at the expense of more established forces.
The Tribune de Geneve meanwhile noted that "the growing strength of the centre resulted in a rejection of traditional parties."
"We expected a small shake-up but it was an earthquake yesterday," said the paper's editor-in-chief in an editorial.