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4 January 2019, 15:41 | Updated: 4 January 2019, 16:54
The man and woman, aged in their 50s, suffered multiple stab wounds in the "random" assault at the station at about 9pm on Monday.
In a statement released by Greater Manchester Police the couple, who have not been named, said: "We would like to thank the men and women from British Transport Police who ran into danger to protect us, as well as the paramedics and hospital employees who have shown great care and skill in looking after us.
"We also want to say thank you to GMP for their ongoing support, our families for their care and concern, our friends and the wider public. We hope this incident does not divide communities or create tensions.
"Now we would like to be left in peace to make a full recovery."
British Transport Police sergeant Lee Valentine also suffered a stab wound to his shoulder in the incident.
In a statement earlier this week, Sgt Valentine said: "We had no idea what we were running towards when we heard the screams on New Year's Eve.
"When we saw the man wielding a knife, instinct took over and we were able to, in company with TravelSafe officers from Metrolink, successfully detain the male."
He and his colleagues, who were on patrol at the station, confronted the attacker with Tasers and pepper spray.
The suspect was heard to shout "Allah" and "Long live the Caliphate" during the incident at the station.
A 25-year-old man who was arrested on suspicion of attempted murder has been detained under the Mental Health Act and is in a secure medical facility, while a counter-terrorism investigation is under way.
Police are said to be increasingly confident that the man acted alone in the final stages of the attack and are investigating whether anybody may have encouraged or assisted him to commit it.
In a statement, the family of the detained man, who live in the Cheetham Hill area of the city, said: "Our thoughts and prayers are with those who were seriously injured, their families and friends.
"We are also eternally grateful for the swift response from the emergency services and the comfort given to those affected by fellow Mancunians and citizens."
The attack happened at the station next to Manchester Arena, where 22 people died after suicide bomber Salman Abedi detonated a device on May 22 2017.