Christian Eriksen remains in a stable condition in hospital pending further examinations, the Danish Football Union (DBU) said in an update to the midfielder's condition on Sunday.
The football world has rallied around Eriksen after he collapsed on the pitch during Denmark's Euro 2020 game with Finland on Saturday.
Eriksen fell to the ground with no other player around him during the first half in Copenhagen.
Team-mates and referee Anthony Taylor called for immediate help from medical staff, with the players forming a protective barrier around Eriksen while efforts were made to resuscitate him.
He was subsequently transferred to hospital, with UEFA saying Eriksen had been "stabilised". The DBU added that he was "awake" and set for "further examinations".
Following a lengthy suspension, the match was resumed and Finland went on to win 1-0.
A DBU statement read: "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 team and the staff of the national team has received crisis assistance and will continue to be there for each other following 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."
One of his Inter team-mates, Belgium striker Romelu Lukaku, showed his support for Eriksen after netting the opening goal in his country's 3-0 victory over Russia.
The striker shouted "I love you Chris" into a television camera having put the Red Devils in front.
And, following his decisive penalty in South Korea's 2-1 victory over Lebanon on Sunday, former Tottenham team-mate Son Heung-min ran to the camera and said "Chris, stay strong, I love you."
Denmark face Belgium in their next Euro 2020 game on Thursday.