President Francois Mitterrand of France declared tonight that his socialist reforms must be carried out "at a good pace" despite complaints from French businessmen and some hesitancy within his own government.

Mitterrand, speaking in a live television conversation with two journalists, said Prime Minister Pierre Mauroy must not slow down application of the Socialist platform of nationalizations, tax reforms and other substantial changes. Mitterrand said slowing the pace of change would violate the mandate he said was conferred on him by the French people in last spring's elections.

The Socialist leader also disclosed for the first time that he has been suffering from still unexplained pains in his back and legs since August. But he discounted published reports that he is seriously ill and said a complete medical report on his health would be published Dec. 15.

His remarks on the economy represented an indirect endorsement of Mauroy's position in a public debate that flared up last week between the prime minister and Finance Minister Jacques Delors, who urged a "pause" in announcing reforms to give the French economy time to digest those already under way.

Mauroy had quickly responded to Delors, saying he planned to forge ahead full speed. Their public exchanges brought to the surface a debate long simmering within Mitterrand's six-month-old government over the economy's ability to absorb swift change without serious disruption.

Mitterrand, responding to a question on the controversy, first said his role was not to arbitrate and underlined his esteem and "personal friendship" for Delors, an economist and high adviser to previous governments. Then, in terms similar to those used by Mauroy in refuting Delors earlier, he added:

"Those who chose us, they want change. And for change, there must be reforms. And these reforms must go forward at a good pace, reasonably, but at a good pace, and without stopping."

The president, speaking in a book-lined room in the Elysee Palace for just under an hour, emphasized the government's decision to carry out major reforms by decree in the coming months to avoid the delays of parliamentary debate with a right-wing opposition eager to throw up procedural obstacles.

"Stopping while it the Socialist program has not even been voted in yet, that would seem stupid to me," he added. "And in any case, we would not be respecting the contract we signed with French citizens, or at least the majority of them."

He declared that the very business concerns that prompted Delors' call for a pause should instead be met with swift execution of the entire Socialist program so "the rules of the game" will be settled and clear. Confusion over Socialist measures to stimulate the economy has been a major business complaint and tonight's television appearance -- the first of its kind for Mitterrand as president -- was designed in part to calm such worries.

In a clear warning that complaining would not dissuade him, he added: "I am not trying to reassure business leaders. I am explaining my policies to them."

Mitterrand sat stiffly before his two questioners, whom he chose personally, according to reports in the French press. Although he appeared to be in good health, he acknowledged publicly for the first time that he is suffering from an ailment beyond the lumbago long known to bother him occasionally.

Press reports disclosed last month that Mitterrand underwent a thorough medical examination at a Paris hospital under an assumed name, entering through a side door in secret and acknowledging the exam only after it had been reported. This led to a round of speculation on his health, along with reminders of former president Georges Pompidou's decline and eventual death in office while the state of his health was withheld from the French public.

Although the examination was presented by presidential spokesmen as a routine check, Mitterrand tonight said he had been suffering from unexplained pains in his back and legs since August.

"I think that, as things went on, it was no longer possible to keep to lumbago as the only explanation," Mitterrand said.

He was given a full examination to determine the origin of the pains, Mitterrand said.