The Super Puma crashed at around midday on Thursday near the hospice on the remote mountain pass, killing both pilots.
A third person described as a ‘flight assistant' was injured in the crash, which happened just after the helicopter's passengers – including four French military inspectors – had been dropped off on the ground.
On Thursday the Swiss defence military said in a statement all Super Puma flights had resumed after initial investigations confirmed that no technical fault was to blame for the crash.
The military has opened an investigation into the crash, the cause of which is not yet known – though some Swiss media outlets reported that the aircraft hit power lines.
The defence ministry did not name the dead pilots, though a commune in the canton of Zurich confirmed that one of the two was a 50-year-old father of three who lived in the town, reported news agencies.
The injured flight assistant is doing well in hospital, an air force spokesman told the media in a press conference on Thursday.
The helicopter's passengers – including the French inspectors, their Swiss counterparts and passers-by – were able to get the three military personnel out of the helicopter immediately after the crash, said air force chief Pierre de Goumoëns, who thanked them for their “exemplary behaviour”.
Defence minister Guy Parmelin, who visited the crash site on Wednesday, said he was “deeply affected” by the drama and his thoughts were with the families of the dead pilots and the injured man.
Je suis profondément touché par ce drame. En pensées avec les proches- VBS - DDPS (@vbs_ddps) September 28, 2016
des pilotes disparus et l'assistant de vol blessé. CF #GuyParmelin
The four French inspectors, who were uninjured, were in the process of carrying out an inspection of Swiss military facilities under an agreement between member states of the Organization for Security and Cooperation in Europe.
Since the beginning of the year Switzerland has also been inspected by Luxembourg, Malta, the US, the UK and France, the defence ministry said in a statement.
Switzerland, meanwhile, has inspected Kyrgyzstan and Finland this year, it said.