Was there a priest on the Titanic who stayed on the ship giving confession to as many as he could?

It would appear to be true, according to this Wikipedia entry.

... passengers and crew headed to the stern, where Father Thomas Byles was hearing confessions and giving absolutions,

Edited with suggestion from @sempaiscuba

This BBC report adds that Father Byles refused to leave the ship, and stayed to comfort passengers, leading recently to calls for his canonisation as a martyr.

Major Edit

I am very reluctant to edit an answer which has a) been accepted and b) been generously up-voted, but in view of all the comments/criticisms (now, thankfully, moved to chat), I feel I have to address the issues raised. All the quotes from contemporaneous documents can be found here if anyone wants to check my work! All emphases mine.

The questions raised vis-a-vis my original answer were three:-

1. Fr Byles (or the Revd Mr Byles, if you prefer) did not administer the Catholic Sacraments to those left on the Titanic.

2) He did not refuse a place on a lifeboat, choosing to remain and comfort those left behind.

3) He was not a martyr, narrowly defined as someone executed for refusing to deny the Christian faith.

I shall take these in order. (NB Roussel was Fr Byles first name; he took the name Thomas on being received into the RC Church.)

1) Administering the Sacraments

(NEW YORK TELEGRAM - April 22, 1912)

Miss Agnes McCoy, a patient in St. Vincent's Hospital, suffering from her privations in the Titanic disaster, gives this account of the last minutes of Father Byles, a Catholic priest. A German priest assisted Father Byles, she said. Those remaining on board the Titanic when the last lifeboat had gone seemed to have consolation, she said, in having a clergyman offer up prayers for them.

"I did not see the final minutes of Father Byles," said Miss McCoy. She had seen him hearing confessions and administering the last rites of the Church in the early part of the disaster. She herself had appealed to him. Survivors told her later of what they had seen as they were washed off the deck. One told her that Father Byles stood and the men kneeled in the water as he offered up prayer.

2) Refusing a place on a lifeboat

(Letter from Fr Byles' brother, William, dated 21 April 1912)

(We) went to St. Vincent's Hospital, when we met first some young boys and afterwards some girls who had been on the Titanic. There were a large number of the survivors there,... After the accident Roussel appeared on deck in full clothes and moved about among the crowd from group to group giving absolution (without confessions) and starting all the Catholics on the Rosary. One girl said the sailors wanted to put him into a lifeboat, but he refused, and went on with his work.

3) A martyr or not?

In my original answer, I referenced the BBC News report, quoting the then (2015) Priest of Fr Byles' former parish, who referred to him as a "martyr" He was not the first.

(Letter to William Byles from the Jesuit Vicar General, on behalf of the Bishop)

Bishop's House Aug. 28, 1912 My dear Mr. Byles,

Last mail brought me the obituary card of your dear Rev. Brother; I have prayed for him, but to tell the truth, I am much more inclined to ask him to pray for me, to get through his intercession strength always to perform my Duty as he performed his. He died a Martyr of charity, performing the most perfect act of love of God and of his neighbor. "Majorem caritatem nemo habet, ut animam tuam ponat quis pro amicis suis." Ergo, how should his soul not have gone straight to heaven. ... I have still to congratulate you on your marriage. The first information I had of the happy event was when I read in some paper that His Holiness the Pope had given you & your wife his blessing. A marriage blessed in heaven by a martyr-brother, & on earth by the Vicar of Christ, is sure to be a happy one...

Very Sincerely Yours J. Cooreman, S.J. Vic. Gen.

I apologise for the length of this edit, but it seemed the only way to satisfy those commentators who appeared determined to believe Thomas Byles was merely another unfortunate man who, unwillingly, went down with the Titanic.