Syria last month dismissed a UN report implicating Syrian officials in the murder, saying it was politically motivated.
But on Monday, the official news agency Sana reported that al-Shara said: "Syria is keen on cooperating fully with the international investigation committee and installing the appropriate mechanisms to do so."
It did not say if Syria would comply with the inquiry's request to question six Syrian officials in Lebanon, one of whom is a brother-in-law of Syrian President Bashar al-Assad, according to a Lebanese source.
The request by chief UN investigator Detlev Mehlis appeared designed to test Syria's willingness to comply with a Security Council resolution demanding full cooperation with the probe into the 14 February assassination of al-Hariri.
Addressing a meeting of parties allied to the ruling Baathists, al-Shara said: "The work of the international investigation committee should be professional and seek to find the truth." He did not elaborate.
Mehlis, the German prosecutor who won fresh powers from the Security Council to carry on with the investigation, has complained that Syrian security figures interviewed in Damascus in September appeared to give only prepared responses.
Foreign Minister al-Shara: The
UN probe should be professional
The meeting of the National Progressive Front (NPF) also tackled a proposed law to allow the creation of political parties in an effort to widen popular participation in Syrian politics, said the news agency.
Syria's Baath party rules through the NPF, a panel of chiefly left-leaning parties.
On Sunday, Syria's Foreign Ministry received a UN request to interview the six officials.
An unnamed Foreign Ministry official declined to disclose the identities of the people the UN investigators want to question or say whether the United Nations wanted to question them in Syria.
Faisal Kalthoum, a member of the Syrian People's Council (Parliament), confirmed to Aljazeera that the Syrian Foreign Ministry had received the UN request.
Kalthoum said he did not know who was sought by the commission for questioning.
But a Lebanese official close to the UN commission said on Saturday that the investigators did want to see General Assef Shawkat, al-Assad's brother-in-law, among others.
The Security Council gave Mehlis
the right to question anybody
The pan-Arab newspaper Al Hayat reported on the weekend that among the Syrians that Mehlis wanted to question were Shawkat; Major-General Bahjat Suleiman, a former chief of Syria's internal intelligence; and Brigadier-General Rustum Ghazale, the Syrian intelligence chief in Lebanon when al-Hariri was assassinated on 14 February.
"Syrian Foreign Ministry will decide on this issue as soon as possible in the context of full cooperation with the case to reveal the truth," Kalthoum said.
He expected Syria to accept all UN requests, unless they were "unachievable demands that directly target Syrian authority and exceed the context of revealing the truth".
"Publicly, Syrians want their government to reveal the truth as this case basically serves Syria," he said.
"However, if the requests target Syrian sovereignty through the probe committee, I believe Syrian public opinion would reject any negative influence on the sovereignty," he added.
Kalthoum said the Syrian government should deal with this case in accordance with the Syrian public opinion.
"The Syrian public opinion fears that this committee may exceed the limits of acceptable demands.
"If the issue of revealing the truth and the techniques of the probe both fall in the context of possible rules, this would ease the cooperation of the Syrian government," Kalthoum said.
"The Syrian public opinion fears that this committee may exceed the limits of acceptable demands"
Syrian People's Council member
"However, Syrians still doubt the orientation of this committee."
In an interim report to the UN Security Council last month, chief UN investigator Detlev Mehlis named Shawkat and the president's younger brother, Maher Assad.
The interim report accused the Syrian government of cooperating with the commission only to a "limited degree" and said its representatives attended meetings in which the investigators questioned Syrian officials about the assassination.
Last week the UN Security Council passed a resolution that upgraded the powers of commission, giving Mehlis the right to question anybody at any location and under conditions of his choice.
The resolution demanded that Syria cooperate fully with the commission and warned the country of further measures if it failed to do so.
Many Lebanese believe Syria was involved in the assassination of al-Hariri, an accusation Syria has denied.