Since winning government, Mr Morrison has commented on asylum seeker issues only at official weekly briefings of Operation Sovereign Borders.
It is understood a boat carrying asylum seekers arrived in Darwin earlier this week, but the Immigration Department has not commented on it.
The Opposition has used the new Parliament's first Question Time to try to find out some details.
Deputy Opposition Leader Tanya Plibersek asked: "Can the Prime Minister confirm whether Australia has approached Indonesia for a people swap deal or should we just wait and read about it in the Jakarta Post [newspaper]?"
Tony Abbott repeated the answer he gave to the media yesterday, saying: "What we are specifically talking about is how we can best handle the question of people who are picked up by Australia in the Indonesian search and rescue zone".
Opposition immigration spokesman Richard Marles followed up by asking for details about "a boat carrying Somali asylum seekers that arrived on Monday evening in Darwin".
Mr Morrison responded with an explanation about why he would not provide Parliament with an answer.
"This Government is not running a shipping news service for people smugglers," he said.
To give an answer that is simply saying they have a media strategy to not do that completely undermines the importance of Question Time and ministerial responsibility.
Labor frontbencher Tony Burke
"As promised, we are running a military-led border security operation."
Labor frontbencher Tony Burke protested, saying that answering questions in Parliament was "the fundamental of why we are here".
"To give an answer that is simply saying they have a media strategy to not do that completely undermines the importance of Question Time and ministerial responsibility," he said.
But the minister argued that providing information publicly - outside of the weekly briefing - would be used by people smugglers to continue their trade.
"The information that was provided by the previous government to provide a proof of voyage. It can also be used to decipher the posture of border protection assets. It can be used to identify potential client pools, especially when nationalities are referred to," Mr Morrison said.
"Now, Madam Speaker, I am not going to be part of a process as a minister that helps people smugglers.
"We are going to hold the line."
Less time for debate in Question Time
The Government has also pushed through new House standing orders shortening the time available for policy debate and scrapping the use of supplementary questions in Question Time.
And new Speaker Bronwyn Bishop - who this morning ruled that it was acceptable for MPs to refer to Opposition Leader Bill Shorten as 'Electricity Bill' - has been given the power to rule on whether MPs are being misrepresented, instead of MPs themselves levelling the accusation.
"I think all sides of the House are sick of that pantomime," Leader of the House Christopher Pyne told Parliament.
"To remove that so that the Speaker will be able to decide that it is disorderly if a misrepresentation has been corrected, for it to be continuously made - I think that will improve the atmosphere of the chamber."
But Labor's Mr Burke says the Government is trying to silence MPs and "censor" political views.
"This automatically involves the Speaker in making a political judgement call on the merits of an argument," he said.
Independent MP Bob Katter says the Coalition is bent on stopping outbreaks of dissent on its own benches.
"You are trying to muzzle your backbench and people on this side of the House," he said of the Abbott Government.
Greens MP Adam Bandt says some of the achievements of the previous parliament - including protection for whistleblowers and the framing of the national debate on gay marriage - only came about because MPs were given time to debate the issues.
"Tony Abbott intends to turn Parliament back into a closed shop," he said.
Bandt refers to Abbott as 'Typhoon Tony'
The term 'Electricity Bill', coined by the Prime Minister, has not been heard again in the chamber since Mr Pyne used it this morning and Mrs Bishop ruled it in order, triggering an Opposition dissent motion that failed on party lines.
The House Standing Orders state that "a Member shall not be referred to by name" and that "a Member must not use offensive words against ... a Member".
Making a point of the Speaker's ruling during Question Time, Mr Bandt referred to the Prime Minister as "Typhoon Tony" without protest.
However, Health Minister Peter Dutton was forced to withdraw his direct use of the given name of Deputy Opposition Leader Tanya Plibersek. That was deemed unparliamentary.