Karami's aide, Khaldun Sharif, said on Tuesday that the former premier and current premier-designate would step down because he had failed to create a national unity government.
The pro-Syrian official resigned on 28 February in the face of a wave of protests sparked by the killing of former prime minister Rafiq al-Hariri in a bomb blast two weeks earlier.
But on 10 March, President Emile Lahud invited Karami to form another government.
Aljazeera's correspondent in Beirut, Ghassan bin Jiddu, said Karami would make an official explanation as to why he would decline to form a new national unity government after meeting the parliamentary speaker Nabih Birri on Wednesday.
Bin Jiddu said Karami had implied it was impossible to balance foreign interests in Paris and Washington with the interests of leading political parties in Lebanon, so he was not in a position to set up a government.
The correspondent added that Lahud would likely consult MPs on the situation on Thursday and may have to back a leadership that would not necessarily form a national unity government.
In a related development, the general in charge of Lebanese military intelligence - whose resignation the opposition is demanding - stepped aside on Tuesday by taking a one-month leave, a military official said. He is not expected to return to duty.
Major-General Raymond Azar, the director of military intelligence, took a one-month "administrative leave", a government official said.
The anti-Syrian opposition had been demanding the resignation of Azar, four other generals and the prosecutor-general.
The head of intelligence in the Mount Lebanon province was appointed to fill the post in Azar's absence.