Vatican spokesman Joaquin Navarro-Valls also confirmed reports no ransom had been paid.
Cesare Baldoni is an editor with Misna, an Italian missionary news agency. He spoke to reporters in Rome today: "He appears to be well, in excellent health. He returned to the diocese in good health and there were no problems."
Casmoussa was kidnapped yesterday by gunmen in two cars in the Al-Majmua Al-Thaqafiyah district of Mosul, Iraq's third largest city and its Christian center.
The Vatican, which opposed the U.S. invasion of Iraq, called the abduction a "terrorist act."
Casmoussa is the head of a 35,000-strong Syrian Catholic, or Chaldean, church in Mosul. The Syrian Catholic Church observes the Liturgy of St. James, performed in Syriac, an eastern dialect of ancient Aramaic, which is believed to be the language Jesus Christ used. It is practiced mostly in Iraq and Lebanon and has pledged its allegiance to the Roman Catholic Church since the 17th century.
Almost all of Iraq's Christian denominations -- Assyrian, Syrian, Armenian, and Greek -- recognize the supremacy of the Holy See.
The motives of the abduction are unclear, but it came amid mounting violence in the run-up to this month's parliamentary elections. William Warda, a spokesman for Assyrian Democratic Movement, a Christian political party, suggested the abduction might be an attempt to intimidate the community into staying at home on polling day.
Kamran al-Karadaghi, an expert on Iraq at the Institute for War and Peace Reporting in London, agrees. He said the abduction was clearly engineered to frighten the whole Christian community in Iraq, especially before the elections planned on 30 January.
"It is also [done] to create more fear and chaos before the elections. But probably, I think this is part of the [broader] campaign against the Christian minority in Iraq," al-Karadaghi said.
Iraqi Christians have kept a low profile recently, even canceling midnight Mass at Christmas, as violence against them has grown. The attacks started in August when several people were killed in Mosul. In October and November, several Christian churches were attacked in Baghdad.
Al- Karadaghi said Christians are one of the oldest communities in the country. He said they make up a very important component of society and are part of a long history and culture. "Christians in Iraq were always really a very important component of the Iraqi society, especially the Assyrians," he said. "In this area, in the Mosul area, they are really an ancient nation, which at one time ruled the entire Iraq. Christians are not somebody who [came recently], not a community, which just appeared or came to Iraq, not at all. Christianity in Iraq appeared much before Islam came to Iraq."
After Mosul, Baghdad is the second-biggest Christian center with many churches, charity organizations, and political parties. Father Louis al-Shabi of St. Josef's Chaldean Church in Baghdad told Reuters television the Christians in Baghdad had prayed for the release of Archbishop Casmoussa.
He said he hopes the future Iraqi government will also do something substantial to return the feeling of security to the Christian community. "We hope the new government will show full support to all Iraqi sects without discriminating between any religion or nationality," al-Shabi said.
In December, the Vatican's foreign minister warned that anti-Christian feeling was spreading in Iraq and other Muslim countries because of the war on terrorism.
Baldoni of missionary news agency Misna said Archbishop Casmoussa and other Christians will not be intimated by the growing violence. "He will stay in Mosul. There is no escape planned by him or others from the Christian community, despite the difficulties of these times," Baldoni said.
But evidence suggests that more and more Christians are fleeing Iraq. Estimates vary widely and exact numbers are not available. However, the Vatican estimates as many as 15,000 Christians have left since the end of summer. Iraq had 1.4 million Christians according to the country's most recent census, which was conducted in 1987.
[For the latest news and analysis on Iraq, see RFE/RL's webpage on "The New Iraq".]