The statement said officials would also consider a separate appeal to increase the number of members on the investigative panel and soon ask the Israeli cabinet to render a formal decision.
But it did not touch on Tirkel's request for the commission to be granted powers to recommend sanctions against political or military leaders.
Shortly after the commission launched its probe on Monday, Tirkel, a former supreme court judge, issued a statement saying that Binyamin Netanyahu, the prime minister, and Ehud Barak, the defence minister, may be called to testify about the raid.
William Schabas, the director of the Irish Centre for Human Rights, told Al Jazeera that while the commission would probably be granted the powers, subpoena is rarely used as inquiries do not often "get much out of unco-operative witnesses".
But he added the inquiry's main flaw "is that they have no intention of bringing the soldiers who were involved in the military action before the commission".
Schabas, who is also an officer at the Institute for International Criminal Investigations, said whether the soldiers behaved with proportionate force is "at the core of the legality" of the raid.
"The only way you can really give an answer to that is to call the people who were actually there on the ships and the soldiers to see what their determinations were, and they're not going to do that.
"So I think a big piece of what we need to know is going to be missing."
In the May 31 incident, Israeli troops boarded the lead ship of a Gaza-bound flotilla and shot dead nine of the activists on board.
Israeli officials insist the troops acted in self-defence after being attacked by some of the activists who they claim were armed with knives and clubs.
Israel established the inquiry after a widespread international condemnation against the raid, but rejected a United Nations proposal for an international probe.
In addition to Tirkel, the panel includes an Israeli expert on international law, a former general, and two foreign observers.
The two foreign observers are David Trimble, a Northern Ireland politician and Nobel Peace Prize laureate, and Ken Watkin, a Canadian jurist.
Meanwhile, the AFP news agency said a forensic report released on Tuesday of the autopsies of the nine activists killed revealed all but two of them were shot more than once and five died from bullet wounds to the head.
The examinations were carried out in Turkey by the government-run Forensic Institute and the reports were made available by lawyers of the the victims' families.
"The findings make it clear the Israeli forces shot to kill the activists and not to overpower them," Yasin Divrak, one of the lawyers, said.
The nine volunteers were shot a total of 31 times, according to the documents.