"Our thoughts are with the Kennedy family who have long and close ties with Ireland at this very trying time for all of them," Prime Minister Bertie Ahern was quoted in the Irish Times newspaper as saying.
The Kennedy family is descended from Patrick Kennedy, a peasant farmer who left Ireland to escape famine and traveled in 1849 to Boston in the United States.
The family has long nurtured its links with Ireland -Jean Kennedy Smith, sister of assassinated U.S. President John F. Kennedy, was U.S. ambassador for five years in Dublin until 1998. Kennedy family members, among the estimated 40 million Americans who claim Irish ancestry, make regular visits.
The town of New Ross, near the Kennedy ancestral home at Dunganstown in County Wexford, was unusually subdued over the weekend as all its churches held Masses for the family, the Examiner newspaper reported.
Patrick Grennan, John F. Kennedy Jr's Irish cousin, recalled the stories of the former U.S. president's son who visited Dunganstown in 1967 with his mother, Jackie Kennedy.
"He ran in from the farm saying there was electricity in the grass and all because he got stung by the nettles," Grennan was quoted by the Irish Times as saying.
"[Jackie Kennedy] visited the homestead and then sent the children back the next day, barefoot, to experience authentic farm life," Grennan said.
The newspaper said there were more visitors than usual on Sunday to the John F. Kennedy center in Dunganstown. The center was expected to close as a mark of respect if John F. Kennedy Jr's death was confirmed, the Irish Times said.
Kennedy, whose father staged a presidential visit in June 1963 to Ireland, visited the country in 1997 and interviewed Sinn Fein President Gerry Adams for George, the glossy political magazine he began publishing.
He caused controversy by attending the funeral of Patrick Kelly, an IRA member convicted in Britain of involvement in a bomb plot against Princess Anne, the Irish Times said.
In Britain, reports CBS News Senior European Correspondent Tom Fenton, the dark days of the Kennedy family touch a raw nerve.
"Everybody puts it in comparison with Diana because of the American royalty side of things," said one woman. "It is a shame because that familys been through so much."
Many of the newspapers report that princess Diana saw John F. Kennedy Jr. as a role model for her own sons - someone who could walk in the full glare of publicity and keep his balance.
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