With a widely loathed palace being rebuilt in the city centre and a new airport whose completion is perpetually delayed, Berliners have become increasingly cynical about the cranes dotting their skyline in recent years. But an ambitious new building project has the potential to change their minds.

A group of Christians, Muslims and Jews is trying to crowdsource funds to build a place where they can all worship: Berlin's "House of One" is aiming to become the world's first building to combine a church, a synagogue and a mosque under one roof.

The competition to design such a project was won by the local firm Kuehn Malvezzi in 2012. Their proposal was for a modernist structure in which the three religions could pray in three separate rooms. A fourth room with a 32m-high domed roof, joining the prayer rooms, would host regular discussions and meetings between the three communities.

One key aspect is that all three religions will be allocated the same amount of space: "One way would have been to try to find the lowest common denominator among the three religions", says Roland Stole, House of One's project manager. "But we want to let each religion live out its faith fully and start developing respect for other belief systems from there".

The decision to crowdfund the building comes from a similar philosophy. Berlin's Christian community, which makes up roughly 37% of the city's 3.3m population, is by far the biggest and most well-funded, while the small Jewish community (0.3% of the population) is notoriously cash-strapped. Had big donors been asked to come on board, the power balance would inevitably have shifted.

Instead, anyone can purchase a symbolic brick for €10 a piece via the House of One website. The initiative hopes to gather €43.5m euros by the start of 2016 – three weeks after its launch, 378 individuals have donated €18,700.

"Having lots of smaller investors rather than one big donor makes us more flexible," says Stolte. "And we don't want this to be just about money, but also about building up a community of people interested in inter-faith dialogue."

The project has already animated admirers and critics alike. Some say it isn't as novel as it claims to be: the Tri-Faith initiative in Omaha, Nebraska, is aiming to construct a campus for three religions by 2015.

It has its detractors in Berlin, too. Martin Mosebach, a prominent novelist and Catholic, has criticised what he sees as the proposed building's lack of a "sacred" dimension, claiming the plan looked as shapeless as a "pharaoh's grave". Parts of the Jewish community too are said to have expressed their reservations.At the start of the initiative, the organisers struggled to find a Muslim organisation willing to come on board: many were nervous about the public exposure involved. The organisation that did join, the Forum for Intercultural Dialogue (FID), mainly represents Turkish-speaking Sunni Muslims – only a small segment of Berlin's Muslim community.

FID's honorary chairman is the controversial US-exiled cleric Fethullah Gülen, a former-ally-turned-arch-nemesis of Turkish prime minister Recep Tayyıp Erdoğan, whose early sermons from the 1990s contain statements on Judaism and Israel that have been interpreted as antisemitic.

Ercan Karakoyun, the director of FID, has rejected the criticism, saying that Gülen's "view of the West, Israel and the US was the mainstream view propagated by the Kemalist regime in Turkey in the 90s".

If they fail to raise €43.5m, the plan's initiators say they will go ahead anyway. €10m would suffice to build a basic version of the building, and if they fail to reach that target, the money will be spent on projects that "contribute to the understanding between religions".