The United Nations Relief and Works Agency (UNRWA) was established after the war surrounding Israel's creation in 1948, when around 700,000 Palestinians fled or were expelled.
But Swiss Foreign Minister Ignazio Cassis pointed out that the number of Palestinian refugees living in Lebanon, Jordan, Syria, the West Bank and Gaza has swelled to more than five million.
"It is unrealistic that this dream (of return) will be fulfilled for all," he said in an interview given to several German-language papers owned by the Swiss NZZ group and published on Thursday.
"But UNRWA maintains this hope. For me, the question is whether UNRWA is part of the solution or part of the problem," he said, concluding that "it is both".
The UN agency, he said, "worked as a solution for a long time, but today it has become part of the problem."
Fuelling the conflict?
"It provides ammunition to continue the conflict. For as long as Palestinians live in refugee camps, they will want to return to their homeland," he said.
"By supporting UNRWA, we are keeping the conflict alive."
The largest demonstrations coincided with the move of the US embassy in Israel from Tel Aviv to Jerusalem on Monday, which saw Israeli forces kill some 60 Palestinians, pushing the overall toll well over 100.
UNRWA is meanwhile struggling to cover a massive budget shortfall, after major donor Washington slashed its 2018 funding.
The administration of US President Donald Trump has opted to cut the $360 million offered in 2017 to a commitment of just $60 million this year, leaving UNRWA scrambling to raise nearly half a billion dollars to guarantee services until the end of the year.
Switzerland is among a group of countries who together pledged about $100 million in March to help fill the shortfall.
Despite his scepticism of the role UNRWA is playing in the Middle East, Cassis warned the sudden funding cut facing the agency posed "a big risk".
"Millions of Palestinians could take to the streets," he said, cautioning that lacking funds could cause the breakdown of a "machinery that provides stability".
"This is a risk that Switzerland cannot afford," he said.
Cassis said his country would continue funding UNRWA, but he also called for a heavier focus on integrating Palestinian refugees into their host communities.
He said for instance that "instead of supporting UNRWA schools and hospitals, we could help the Jordanian institutions promote integration of Palestinian refugees."