The MPs move to impeach the National Directorate of Security Afghanistan, Masoom Stanekzai, last week has sparked sharp criticism by some lawmakers who said signatures gathered over the move had been "collected illegally".
"Mr Speaker, I hope that this session will not move towards a rift. Review your decision, otherwise this is the house of people and we will not let any ‘bullyingí happen here," said Mohammad Nazir Ahmadzai, an MP.
"The chiefs committee is trying to include the summoning issue into its agenda instead of discussions on other matters," MP Mirwais Yasini said.
Other MPs, who signed the petition to move to impeach the NDS chief, said their actions had been in accordance with the law.
"Some people are acting against my decision because I have done my job based on the internal duties principle and in accordance with the Constitution," Humayun Humayun, the first deputy speaker of the parliament, said.
"Supporting ‘illegalí acts of government is not fair for a peopleís representative," said Zahir Qadeer, an MP from Nangarhar.
The Wolesi Jirga, Lower House of Parliament, Speaker Abdul Rauf Ibrahimi meanwhile defended the decision to move to impeach the NDS chief.
"Fifty MPs have signed (the petition) here (in the house) and have sent it to the chiefs committee," Ibrahimi said.
This comes after MPs said this month that a surge in attacks in the country in recent months, particularly in Kabul, was due to Stanekzaiís "incompetence" - a claim Stanekzai himself has rejected.
On April 7, the Wolesi Jirga summoned Stanekzai to answer questions over security concerns. However, the session was held behind closed doors.
Before heading to the session, Stanekzai said due to the current situation in the country, he could not discuss matters publicly as "I will explain issues in one way which will be misinterpreted the next day".
The NDS chief was expected to be asked about the airstrike in Dasht-e-Archi district in Kunduz, the Taliban attack on the Intercontinental Hotel in Kabul, and other recent insurgent attacks. But the MPs did not raise such questions, according to an MP who talked after the session on April 7.
However, one MP said Stanekzai had presented convincing statements during their closed session.