A top-ranking official of the Libyan government has hinted that cooperation coming from detained Australian lawyer Melinda Taylor and the International Criminal Court (ICC) is the key for the early resolution of the ongoing diplomatic row.

Libya's Deputy Foreign Minister Mohammed Abdel Aziz told Reuters over the weekend that his government is "committed to solving this problem speedily but what we need is the cooperation of the International Criminal Court."

Mr Aziz added that Tripoli looks forward to more acceptable behaviour coming from Ms Taylor, who he noted has so far refused to answer questions posed to her by Libyan probers without the presence of a legal representative, purportedly coming from the ICC too or from an independent international body.

Amidst indications that Ms Taylor's recent detention was decided independently by Zintan authorities, Mr Aziz insisted that the country's attorney-general has been overseeing the case and the same office has approved requests for the Australian national to be provided a defence lawyer that she herself has chosen.

Following the brief visit of Australian Ambassador to Libya David Ritchie to Ms Taylor Tuesday last week, the Libyan official disclosed that another team would be allowed to see the Aussie and the rest of the ICC delegates, which supposedly happened last Saturday.

A defence lawyer from the United Kingdom was believed to have joined the second batch of visitors, Reuters said.

"We are hoping that the investigation will be initiated and all parties will cooperate accordingly," Mr Aziz said in expressing optimism that the problem will end before the 45-day period set by Libyan authorities as the necessary time to fully conduct the investigation on Ms Taylor and her ICC colleagues.

Mr Aziz issued the comments as more international bodies joined the Australian government and the ICC in demanding for the immediate release of the detained ICC team.

Canberra and top ICC officials insisted on earlier statements that as official representatives of the ICC in Libya, Tripoli, as a committed member of the international community, should have automatically accorded full diplomatic immunity to Ms Taylor and her team.

The UN Security Council labelled her continued confinement by Libya as a "serious concern," for the international community while NATO Secretary-General Anders Fogh Rasmussen voiced out his strong regret on the incident that led to the incarceration of the ICC staff operating in Libya.

"I would urge them to release these individuals as soon as possible," Mr Rasmussen told media people during a stop in Canberra late last week.

Also, Ms Taylor's parents have appealed on Libyan officials to quickly grant her freedom, stressing in a televised statement that "all we want is the process of law to go ahead and for Melinda to be released as quickly as possible."

But Tripoli appears unfazed by the rolling criticisms on its latest actions as Mr Aziz asserted that "the international community should be fair to Libya."

"You cannot continue to always push Libya to do this, to do that. There is the other side of the coin that has to be addressed too," the Libyan diplomat told Reuters.

He added that grave concerns for the ICC delegates' safety were unfounded, assuring that they were well provided of their daily needs while in Libyan custody and their safety the utmost concern of Zintan officials.

Foreign Minister Bob Carr has expressed alarm on the manner the ICC affair has been handled so far by Tripoli as Australia was left in the dark for days on the whereabouts of Ms Taylor and her team following their arrest during a visit to Seif al-Islam Gaddafi.

Canberra only got wind of first-hand accounts on Ms Taylor when Tripoli finally arranged for Mr Ritchie to see the Aussie last week.

Ms Taylor was accused by Libyan officials of passing secret information to Seif al-Islam and withholding the location of a former Gaddafi henchman wanted by Tripoli.

After receiving the brief from Mr Ritchie, Senator Carr has confirmed reports that Ms Taylor will have to stay a little longer behind bars in Zintan.