The Swiss Football Federation announced that it had decided not pursue its bid to have the St. Jakob-Park stadium in Basel included on the 13-venue list due to be drawn up by the sport's European governing body UEFA.
SFF president Peter Gillieron said the fact that Switzerland hosted Euro 2008 along with neighbouring Austria was a major factor.
"We felt that countries which have organized the European championships over the past 12 years had, at best, a slim chance of being picked for Euro 2020," he said in a statement.
As a result, said SFF secretary general Alex Miescher, the federation did not feel able to make the financial investment nor to muster support from local and national politicians.
Later, Turkey abandoned their bid to try and host the 2020 semi-finals and final, preferring instead to try and win the right to host Euro 2024.
"We believe Turkey is at a point where it can undertake the entire tournament," a Turkish Football Federation statement announced.
The federation said Turkey would soon have 13 stadiums in compliance with the "capacity criteria of the European Football Championship."
"When this is the situation, Turkey is a country that can host such a tournament on its own," it added.
"Therefore, our board has decided today not to bid for the UEFA EURO 2020 semi-finals and final."
The federation said it would now focus on "a campaign for candidacy to host the entire Euro 2024".
Earlier Euro 2016 hosts France pulled out of 2020 with their federation president Noel Le Graet declaring Lyon would not be proposed as a candidate city.
Already this week the Czech Republic and Euro 2012 co-host Poland both withdrew, but Belgium confirmed that Brussels would officially be presented as a candidate city.
UEFA will announce the 13 host cities in September as president Michel Platini puts into place the unprecedented new format across the continent.
Germany, which staged Euro 1988 and the 2006 World Cup, has already entered the Euro 2020 fray, with Munich beating Berlin as the German Football Association's (DFB) candidate city.
The Germans have applied for one of two packages and are hoping to either host three group matches and a quarter-final or are looking to hold the semi-finals and final in the Bavarian capital.
"We are sure we have a strong bid and hope to convince UEFA with our world-class facilities and the enthusiasm of the fans in Germany," said DFB general-secretary Helmut Sandrock.