"I will tell you that [UN chief investigator] Detlev Mehlis wants a special Syrian inquiry. We are ready to carry out this investigation," the Syrian Foreign Ministry's legal adviser Riad Daudi told Aljazeera on Tuesday.
"But Mr Mehlis, who has never made this kind of request before, must tell us exactly what kind of inquiry he wants us to do," he said.
"We will examine with Mr Mehlis what kind of cooperation he wants during our next meeting ... We don't have any problem with this as long as it is done in a manner that respects our sovereignty."
Earlier, Mehlis had invited Syria to launch its own investigation into the killing to deal with unanswered questions.
The German prosecutor on Tuesday addressed the UN Security Council on his written report, released last Thursday, that found evidence of Syrian involvement in the 14 February killing of al-Hariri in Beirut.
He had also criticised Damascus for what he called lack of cooperation with his commission.
"... the Syrian authorities may wish to carry out on their part their own investigation into the assassination of Mr Hariri in an open and transparent manner"
UN chief investigator
Mehlis said the extension of his commission's mandate until 15 December would provide another opportunity for Syria to "show greater and meaningful cooperation, and to provide any relevant substantial evidence on the assassination".
"For this reason, the Syrian authorities may wish to carry out on their part their own investigation into the assassination of Mr Hariri in an open and transparent manner," Mehlis said.
"This would enable the commission to fill in the gaps and to have a clearer picture about the organisers and perpetrators of the 14 February terrorist act," he added.
Furthermore, Mehlis told the UN Security Council that his commission "has received a number of threats which were deemed, in the assessment of our security personnel, to be credible".
He said security for its members was a priority.
Mehlis: The level of risk, already
high, will now increase further
He noted that since the inquiry commission began its work, exceptional security measures had been taken to protect it with the help of Lebanese security forces.
"However it should be noted that despite all the precautionary measures, the level of risk which was already high will increase further, particularly after the issuance of the report," Mehlis added.
He called for stepped-up security for his team of 30 investigators from 17 countries.
Shortly before he spoke, US ambassador John Bolton and French ambassador Jean-Marc de La Sabliere said they expected to circulate a joint resolution very soon.
It is likely to demand Syria's cooperation with Mehlis's investigating commission, though how strong the language will be is still being discussed.
Mehlis's investigation has been extended until 15 December and he said his team would interview a number of witnesses, complete its examination of recently obtained evidence, and cooperate with Lebanese judicial and security authorities.
Pressure on Syria
A draft UN Security Council resolution, circulated on Tuesday by the United States and France, threatens Syria with economic sanctions if it does not cooperate with the UN inquiry.
The draft, co-sponsored by Britain, also would impose an asset freeze and travel ban on anyone designated as a suspect in the investigation led by German prosecutor Mehlis.
It also would require Syria to detain any Syrian official or individual considered by the UN investigative team as a
suspect in al-Hariri murder, so that they can be interviewed, Bolton said.
A UN resolution is likely to turn
up the heat on Damascus
US President George Bush accused Syria of destabilising Lebanon and backing "terrorists" and said the UN must hold Damascus accountable.
"Syria is destablising Lebanon, permitting terrorists to use its territory to reach Iraq, and giving safe harbour to Palestinian terrorist groups," he said in a speech at Bolling Air Force Base in Washington.
"The United Nations has passed strong liberations against terror. Now the United Nations must act," said Bush.
"Syria and its leaders must be held accountable for their continuing support for terrorism, including any involvement in the murder of prime minister Hariri," said the US president.
In Moscow, Russian President Vladimir Putin on Tuesday called on the international community to show balance towards Syria on the issue of the UN inquiry into the murder of al-Hariri.
During a telephone conversation with Syrian President Bashar al-Assad, Putin welcomed Syria's stated readiness for "broad cooperation with the international commission investigating the circumstance of the murder" of al-Hariri, the Kremlin press office said.
However, he "underlined the pressing need for balanced action from the international community so as not to allow new flashpoints of tension in the region".