Despite the prime minister previously stating he would want Australia to move away from the monarchy, he said it was too soon to have those discussions.
"Now is not a time to talk about our system of government, now is a time for us to pay tribute to the life of Queen Elizabeth," he told the ABC's Insiders programme on Sunday.
"That's the system of government that we have, it's one which as Australian prime minister, I have a responsibility to respect."
The comments come as King Charles III was proclaimed as monarch at a ceremony at Parliament House on Sunday by Governor-General David Hurley.
The prime minister brushed off questions about when would be the right time to start having conversations about moving away from the monarch.
"Quite clearly, this is a time of national mourning," Mr Albanese said.
"Even though the Queen was 96 years of age and had lived such a long life, it still came as a shock. I think that says something about the way that the Queen was perceived as a constant in our lives."
Former prime minister John Howard said he had no doubt the Queen was pleased when Australia voted not to become a republic during the 1999 referendum.
Mr Howard, who was prime minister at the time of the national vote, praised the Queen's sense of duty and respect while the referendum campaign took place.
"I have no doubt that she was pleased with the result, but she never sought to influence it. She continued to do her job, again and again," he told the ABC's Insiders programme.
Mr Howard also revealed his and the Queen's private secretary shared three draft press statements on potential outcomes of the referendum.
While Australia voted not to become a republic at the time, Mr Howard said the statement in the event of a 'yes' vote would have expressed her love for Australia and desire to see the country succeed.
Opposition Leader Peter Dutton said any talk of Australia becoming a republic would need to be held at another time.
Mr Dutton has expressed his view that Australia should remain as a constitutional monarchy.
"At the moment we mourn the loss of an incredible world leader, a woman who was obviously an amazing role model to many women, to many female leaders across the world," he told the ABC.
"We need a King as much as we did a Queen, because we have a stability in our system that served us well and I don't believe in disrupting that."
