The former Tottenham playmaker collapsed on Saturday during Denmark’s opening Euro 2020 match with Finland in Copenhagen.
Eriksen underwent prolonged treatment on the pitch before he was taken to hospital.
In a statement, the Danish FA said: “Latest news: This morning we have spoken to Christian Eriksen, who has sent his greetings to his team-mates.
“His condition is stable and he continues to be hospitalised for further examination.”
The statement continued: “The team and staff of the national team has received crisis assistance and will continue to be there for each other after yesterday’s incident.
“We would like to thank everyone for the heartfelt greetings to Christian Eriksen from fans, players, the Royal Families from both Denmark and England, international associations, clubs etc.
“We encourage everyone to send their greetings to the Danish FA, where we will make sure they are all passed on to Christian and his family.”
Parken Stadium fell silent soon before half-time when the former Tottenham playmaker dropped to the ground when running to collect a throw-in.
English referee Anthony Taylor immediately called medics on to the pitch and Eriksen underwent prolonged treatment with compressions performed on his chest before he was taken to hospital.
It was later confirmed the Inter Milan player was stable, which allowed his team-mates to resume their fixture in Copenhagen with Finland claiming a 1-0 win thanks to Joel Pohjanpalo’s 59th-minute goal.
“Christian Eriksen is awake and his condition remains stable. He remains hospitalised at Rigshospitalet for further examinations,” a statement from the Danish Football Association read.
National team manager Kasper Hjulmand struggled to hold back the tears during his post-match press conference and revealed they had the choice of finishing the Group B opener on the night or return on Sunday.
“It was more unmanageable to have to restart tomorrow. It was more unmanageable than going back out now and getting it all put behind us,” he said.
“I could not be more proud of this team, who take good care of each other.
“There are players in there who are completely finished emotionally. Players who on another day could not play this match. They are supporting each other. It was a traumatic experience.”
After Eriksen collapsed, his team-mates formed a shield around the 29-year-old while he received treatment and fans from both sets of countries chanted the name of the midfielder.
He eventually taken off the Parken Stadium pitch on a stretcher and was seen to be awake.
Hjulmand added: “All thoughts are with Christian and his family. Christian is one of the best footballers, but he is an even better person.”
UEFA president Aleksander Ceferin said: “Moments like this put everything in life into perspective. I wish Christian a full and speedy recovery and pray his family has strength and faith.
“At these times, the unity of the football family is so strong and he and his family carry with them the good wishes and prayers of everyone.
“I heard of fans of both teams chanting his name. Football is beautiful and Christian plays it beautifully.”
Denmark could have salvaged a draw, but Pierre-Emile Hojbjerg saw a late penalty saved, which would most likely have been taken by usual spot-kick man Eriksen had he been on the pitch.
Leading sports cardiologist Professor Sanjay Sharma has questioned whether the Serie A winner will play again.
“The fact he’s stable and awake, his outlook is going to be very good,” he told the PA news agency.
“I don’t know whether he’ll ever play football again. Without putting it too bluntly, he died today, albeit for a few minutes, but he did die and would the medical professional allow him to die again? The answer is no.”
The BBC issued an apology after images of Eriksen receiving treatment were broadcast during their live coverage before they returned to the studio where pundits Cesc Fabregas, Alex Scott and Micah Richards were visibly emotional.
“Everyone at the BBC is hoping Christian Eriksen makes a full recovery,” a statement read.
“We apologise to anyone who was upset by the images broadcast. In-stadium coverage is controlled by UEFA as the host broadcaster, and as soon as the match was suspended, we took our coverage off air as quickly as possible.”
Presenter Gary Lineker later added: “In 25 years of doing this job, that was the most difficult, distressing and emotional broadcast I’ve ever been involved with.
“Thanks to Cesc Fabregas, Alex Scott and Micah Richards for your professionalism, warmth and empathy. Get well soon, Christian Eriksen.”
England, who get their Euro 2020 campaign under way on Sunday against Croatia, were due to hold a press conference at 6.30pm BST with captain Harry Kane set to be alongside manager Gareth Southgate.
But the Football Association confirmed the media briefing had been cancelled with Kane, who spent eight seasons with Eriksen at Tottenham, writing on Twitter: “Chris. I’m sending all my love to you and your family. Stay strong mate.”
The Duke and Duchess of Cambridge sent a message of support for Eriksen. They posted on the social media platform: “Encouraging news about Christian Eriksen, we are all thinking about him and his family.
“Well done to the medical team and Anthony Taylor for their calm and swift action. W.”
Numerous messages were sent to the midfielder while current club colleague Romelu Lukaku dedicated his first goal in Belgium’s 3-0 win over Russia to Eriksen by saying into the pitchside cameras: “Chris, I love you.”
He later told beIN SPORTS: “It was difficult to play because my mind was with my team-mate. I hope he is healthy and I dedicate this performance to him.
“I cried a lot because I was scared, obviously. You live strong moments together. I spent more time with him than with my family. My thoughts are with him, his girlfriend, his two kids and his family.”
Finland captain Tim Sparv also sent his well wishes on Twitter, he said: “What an emotional roller-coaster this day has been. Our thoughts are with Christian Eriksen and his loved ones during these difficult times.
“Football is so insignificant when something like this happens. Life is precious. Take care of each other.”