Giorgio Napolitano said he was "not interested" in new elections to resolve Sunday and Monday's voting that produced no clear winner, the Italian news agency ANSA reported.
The president, who completes his seven-year term in May, said he would not accept a second term.
"I am convinced that the founding fathers conceived the role of president of the republic as measures in seven-year terms," he told journalists during a state visit to Germany. "It is not a coincidence that no other president has served a second term."
The center-left alliance led by the Democratic Party came in first in the voting, but failed to win a working majority in the Senate.
Pier Luigi Bersani, the leader of the Democratic Party, said Friday he would propose a new government formed around a specific seven or eight items.
Bersani has ruled out forming a coalition with the People of Freedom party led by former Prime Minister Silvio Berlusconi.
"He had opportunities to show one's self to be responsible," Bersani said of Berlusconi. "He has wasted all of them."
Bersani said he has reached out to the anti-establishment 5-Star Movement led by comedian Beppe Grillo. Grillo has said he would not join a government led by either Bersani or Berlusconi.