"This is what the country needs at the moment", he said.
He said he had informed the president about his decision and would resign as premier as soon as party delegates and members elected a new Labour leader. 
His statement was delivered just after thousands once again took to the streets of the capital Valletta urging Muscat to leave his post at once. 
Muscat had faced increasing pressure to quit as people close to him in government were linked to the probe of the assassination of journalist Caruana Galizia, who was killed by a car bomb explosion in October 2017.
The investigative journalist had exposed government corruption in her blog.
Earlier this week, two ministers and Keith Schembri, Muscat's chief of staff, left office after being linked to the investigation. Schembri was arrested on Tuesday and released without charge on Thursday.
Calls had steadily grown louder for Muscat's resignation after Schembri was questioned in connection with the murder.
The premier had been expected to resign Sunday morning after an emergency meeting of his Labour party was called, a high-ranking lawmaker told dpa earlier that day. Reports of cabinet in-fighting have dominated Maltese headlines in recent days. 
At Sunday's protests, the popular newspaper columnist Ranier Fsadni told attendees that "Malta was drowning in mud" and that Muscat had lost all credibility.
Muscat was elected prime minister in 2013 and oversaw impressive economic success and low unemployment but his administration was weighed down by allegations of corruption and cronyism.
In his speech, he did not refer to the public demands for his immediate resignation.
"I am not perfect. And I have my own shortcomings... I assure you I gave everything in return for the trust you gave me. I had my defects and for them I apologise personally, even when these shortcomings were because of someone else," he said. 
Muscat's announcement was met with harsh criticism from many who believe the office has been tarnished because of the link to the murder. 
In a tweet, opposition leader Adrian Delia said the delay in the resignation is a blow to justice and insisted Muscat should leave at once. 
On Saturday, businessman Yorgen Fenech, pleaded not guilty to the charges of complicity in the murder of the journalist, participating in a criminal organization and complicity in causing an explosion.
Fenech had been named as the owner of a secret offshore company called 17 Black, which was intended to funnel money into the accounts of the prime minister's chief of staff, Schembri, and minister Konrad Mizzi. Both resigned last Tuesday.
----------------------------------------------------------------------------------------------