Gilani made the remarks during a meeting with lawyers at his residence in Lahore three days after the Supreme court convicted him of contempt for refusing to act on orders to write to the Swiss government to reopen cases of alleged money laundering against Zardari.
The apex court gave Gilani a symbolic sentence of less than a minute and some legal experts have contended he is not eligible to continue as premier following his conviction.
However, Gilani said only parliament could decide if he would continue to remain the prime minister.
"Parliament is the supreme body in the country. It can decide the issue of a member's disqualification as it is the representative forum of the 180 million people of Pakistan," he said.
Gilani made it clear that he would not resign due to political pressure or to fulfil anyone's wishes. He said "certain elements" were conspiring against him but he was determined to foil all such conspiracies.
While addressing parliament after his conviction, Gilani said he could be disqualified only by the speaker of the National Assembly or lower house of Parliament.
He challenged the opposition PML-N, which has demanded his resignation, to move a vote of no-confidence against him.
During his interaction with the lawyers, Gilani said PML-N chief Nawaz Sharif should not interpret the apex court's verdict on his conviction according to his own wishes. Gilani further said he will appeal the court's decision.