Armed attackers abducted Archbishop Paulos Faraj Rahho as he left the Holy Spirit Church on Friday, while his driver and two bodyguards were killed.
A local priest told the Christian persecution news agency Compass Direct that Christians across Iraq had been left shaken by the abduction.
He added that the kidnappers have demanded a large ransom for the release of the archbishop.
"They want money, but in addition they want to break all the Christians in Mosul," said Father Najeeb Mikhail.
He said that Rahho's health had been badly affected by the stress of constant threats from militant gangs demanding extortion money.
"One day before his kidnapping, they attacked the bishop's house in Mosul and broke many things," Mikhail said, adding that the archbishop had refused to meet the demands of the attackers for money.
The Chaldean Church, which practices an ancient Eastern rite, is aligned with the Roman Catholic Church and recognizes the authority of the Pope.
Following the archbishop's abduction, many of the less than one million Christians in Iraq fear they will be next.
Father Emanuel Youkhana of Christian Aid Program Nohadra Iraq said he expected more Christian families would flee Mosul as a result of the kidnapping, which follows the murder of a Chaldean priest and three deacons last June, and a series of bomb blasts on Mosul churches in January.
"You might release the bishop, but you cannot recover the confidence of the people," Youkhana said. "Within the last two or three months, the church is attacked and then the bishop is kidnapped, so how can people save their confidence?"
Mikhail believes the attacks are not about money but about driving Christians out of the area.
"There are some Muslims that want to put Christians out of Mosul," the priest said. "So through these criminals, they try to intimidate the relationship between Muslims and Christians."
Iraqi Prime Minister Nuri al-Maliki has written to the Chaldean patriarch of Baghdad and spiritual leader of Iraq's Roman Catholics, Cardinal Emmanuel III Delly, expressing his "deep sadness and grief" over Rahho's kidnapping.
In a statement Tuesday, Maliki said, "The prime minister has issued an order to the interior minister and all security officials of Nineveh province to follow the case and work very hard to release [Rahho] as soon as possible."
"The Christian sect in Iraq is one of the basic components of Iraqi society and can never be parted from its people and civilization," Maliki commented in the statement. "Any assault on its sons represents an assault on all Iraqis."
On Saturday, the U.N. envoy to Iraq, Staffan de Mistura, called on the government to "redouble its efforts" to protect religious minorities in Iraq.
Christians make up about 3 percent of Iraq's 27 million, mostly Muslim, population.