He said this while addressing a press conference at the National Assembly on Wednesday.
Since he announced his defection from the APC, the ruling party has been calling on Mr Saraki to leave the post since his new party, PDP, does not have a majority in the Senate.
Reacting to this on Wednesday, Mr Saraki insisted he will remain in his position so long as he enjoys the support of his colleagues who elected him.
“I will not give in (to pressure). I will not. I was elected by members,” he responded to a question on his plan on calls for his removal.
Mr Saraki said he was not desperate for power, and will not cling on to his position should he lose the confidence of his people.
Mr Saraki said if two-thirds of senators passed a vote of no confidence in him, he would honourably bow out. He urged Nigerians not to be under any illusion that he was a power monger as being peddled by his critics.
Mr Saraki also said Speaker Yakubu Dogara would also step down if substantial majority of members of the House of Representatives withdraw their support for him.
Mr Dogara was seated to the left of Mr Saraki, but did not address the press or take questions.
Mr Saraki has faced allegations that he is desperate to retain power, and could betray anyone in the process. Amongst the allegations the lawmaker has faced in recent weeks include a recollection of his relationship with his father.
The late Olusola Saraki was said to have been sent into political oblivion after his son defied him in 2011 to appoint his successor as governor that year.
He also took over the Kwara North Senatorial District seat from his sister, Gbemisola Saraki. The duo remained at political loggerheads ever since.
Even though there were initial reconciliations, the sister recently declared support for President Muhammadu Buhari and the All Progressives Congress after the Senate president defected to the opposition Peoples Democratic Party last week.
Mr Saraki’s politics has been under intense suspicion since he outsmarted the leadership of the APC to become the Senate President in 2015, entering an alliance that saw Ike Ekweremadu, a member of an opposition party, become the deputy Senate President.