Detective chief superintendent Russ Jackson said the release of potential suspects 'can be expected in investigations of this nature as we corroborate accounts that have been provided'.
Police say they are looking for information on Abedi's movements up to four days before the deadly attack.
Rudd declined to comment on exactly what was known about the 22-year-old bomber, during an interview with Sky News.
"This is a different item than the one he used in the attack".
Although detectives have no reason to believe the bag contains anything unsafe, they are warning the public not to approach it, and instead call 999 immediately.
Counter-terrorism police have issued the image as they urge the public to help them track the terrorist's movements in the days before the bombing.
Earlier, police made a 16th arrest in connection with the Manchester suicide bombing at a concert by USA singer Ariana Grande, the deadliest attack in Britain for 12 years.
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"Did you see Abedi with this suitcase between the 18 and 22 May 2017?"
"Did you see Abedi with this suitcase? There remain a number of things that concern us about his behavior prior to the attack and those of his associates which we need to get to the bottom of", Jackson told the Guardian.
A 23-year-old man was arrested in the southern coastal town of Shoreham-by-Sea, more than 400km from Manchester yesterday over the attack claimed by the Islamic State in Iraq and Syria (ISIS).
Meanwhile, Britain's domestic intelligence agency, MI5, launched an internal probe into whether vital clues were missed ahead of the Manchester attack.
Abedi's father and brother have also been arrested in Libya.
Police raided more homes on Monday as the relentless search for the network behind the suicide bombing continued a week on from the attack.
Britain's official terror threat level was set at "critical" in the days after the attack but was downgraded Saturday to "severe".
The attack, which has been claimed by the Islamic State jihadist group, targeted concertgoers at the end of a show by U.S. teen pop idol Ariana Grande.