The claims are thought to constitute a majority of those made as part of the government's restitution plan, under which it intends to hand 134 billion Kč in property and compensation to 16 religious organizations.
Parliament passed a bill November 2012 giving the green light to the restitution and this law, which came into effect January, was upheld by a constitutional court in Brno in June.
While applauded by religious organizations, the plans to return 75 billion Kč worth of property and pay out, over three decades, 59 billion Kč in compensation for unreturned property have come up against opposition from campaigners who say the handover will result in corruption.
Organizations have been given a year to make requests for the return of land or property, although determining what actually should be given back is likely to prove a complex process.
Institutions are expected to show proof of ownership in pre-communist times, although incomplete record keeping and the extensive damage to records from floods in 2002 mean this will be difficult in many instances.
Historians may be used to help verify claims, while the Culture Ministry, the national Land Fund and the forestry company Lesy ČR are overseeing the whole process.
In an Aug. 12 meeting with Prime Minister Jiří Rusnok, who is set to step down after his Cabinet lost a recent confidence vote in the Chamber of Deputies, Prague Archbishop Dominik Duka reportedly said it was important that deadlines already set for the restitution process were met.
According to the Czech News Agency (ČTK), some church officials have complained to media that the process is taking longer than expected. That the more than 11,000 claims made by the Catholic Church make up a majority of claims filed so far ties in with predictions the organization will receive 80 percent of money and property from the process.
Duka has previously indicated that the return of its property could allow the Catholic Church to set up hospices and schools.
The restitution, which concerns land and property seized by the Communists from 1948, and the issue of how it should be resolved, has been a talking point since the Velvet Revolution nearly a quarter of a century ago.
The then-Finance Minister Miroslav Kalousek said in June, after the Brno court upheld the restitution law, that the legislation was "valid and effective."
"Finally, we are the last country of the former Soviet bloc to be able to remove this international disgrace and settle relations with our churches," he said.
While the restitution program is likely to involve large cash handouts to religious organizations, supporters of the scheme say these will come at the expense of grants to these same institutions, so the additional expenditure entailed is less it appears.
Opinion polls however have shown a majority of Czechs, only about 10 percent of whom are Catholics, are against the proposals and an organization, Stop církevním restitucím (Stop Church Restitution) has even petitioned the Vatican to intervene to halt the process.
The Social Democrats (ČSSD) have also been strongly opposed to the restitution.
Opponents of restitution have raised questions about how the Catholic Church acted under Nazi occupation and some have warned of the risk of the "embezzlement" of funds by officials.
The Czech Republic is not the only country where the restitution of church property confiscated during the Second World War has been in the news in recent weeks.
A number of US congressmen have recently called on US Secretary of State John Kerry to press the authorities in Romania to speed up the restitution process of confiscated Hungarian church property, after a law was passed increasing from five years to 10 years the delay before property is returned.
In response, politics.hu reported, the US Department of State last month released a letter in which Acting Assistant Secretary for Legislative Affairs Thomas B Gibbons said ensuring the restitution issue in Romania was dealt with was "a priority" for the US administration.
More than 2,000 buildings in Romania were confiscated from several churches, along with actual church buildings and nearly 2,000 Jewish-owned properties.