The pair were part of a 22-strong squad that travelled from Durham City club last Thursday.
A spokeswoman for the Foreign Office said it was assisting families of two British men.
Thomas Andrew, who played for Durham-based Clems Pirates RFC, collapsed after complaining of breathing difficulties on Sunday night.
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The deceased player and his friend had returned to the hotel in the early hours of Sunday and had experienced difficulty breathing by Sunday morning.
British media were giving the story heavy coverage, with The Times reporting on Tuesday that "local police said that they were investigating links to "narcotics and liquor".
Howard's death was confirmed in a club statement issued on Monday.
"We would also like to take this opportunity to thank everyone for the many messages of sympathy and support that have been received from our members, friends and the wider rugby family; they are very much appreciated at this hard time".
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The second of the two rugby players, who was under treatment in the Intensive Care Unit of a leading private hospital in Colombo has passed away a short while today (15).
Police said an autopsy on Howard revealed that he did not die due to any external injuries or any illness.
They had played one game on Saturday with CR & FC in Colombo and following the game several members of the team had visited a nightclub in Colpetty.
"The spokesman added that a judicial medical officer had given an open verdict" on the deaths and further forensic tests are being carried out". It added: 'The work in Galle will continue the worldwide charity work began by Clems Pirates in South Africa in 2004'.
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May's spokesman, however, said the "focus is on getting this right" rather than meeting a deadline. It would make a lot of other problems that are hard to solve right now...
"We will also continue to support the Clems Sri Lankan tour party by being in regular contact with senior club officials out in Sri Lanka".