Fuad Siniora, the Lebanese prime minister, said on Tuesday: "This is an extremely painful situation, and I have asked the International Committee of the Red Cross (ICRC) to follow this tragedy closely.
"We want to discover the whole truth."
Rights group Amnesty International said it had received reports that the "exhumations are not being carried out with the appropriate level of care, and there are fears that the bodies may be damaged and potential evidence lost".
It said the work should be done in line with international standards set out by the UN.
Amnesty further urged Lebanon to take immediate actions to ensure the evidence at the sites is properly preserved, that the victims are identified and that the evidence is used to bring suspected perpetrators to justice in fair trials.
The remains of the 30 people were exhumed on Saturday and Sunday from two mass graves near the village of Anjar, 3km from the border with Syria.
The Syrian army had its intelligence headquarters and a prison there during its nearly three-decade military presence of its smaller neighbour, which ended in April.
Syrian troops left Lebanon under
intense international pressure
Said Mirza, the attorney-general, said that among the remains "were those of women and children", and he also called on the ICRC to join in the inquiry. He added that the government would not hesitate to call on outside experts.
The remains have been sent to Beirut for examination by forensic pathologists.
Ghazi Aad, an official from the Support of Lebanese in Detention and Exile (Solide), visited Anjar on Sunday and demanded an international investigation to find the identities of those buried in the mass graves.
Aad said he was satisfied with the opening of a judicial inquiry, but added that the case presented "a humanitarian matter that must not be obstructed".
Solide has unsuccessfully called for the release of 100 Lebanese prisoners it says are proven to be currently in Syrian jails. Syria has denied the allegation.
"Exhumations are not being carried out with the appropriate level of care, and there are fears that the bodies may be damaged and potential evidence lost"
The fact the Anjar remains were in bags and not buried according to any religious rites indicated the people may have been killed.
An Anjar resident who requested anonymity told AFP: "Prisoners who died in the Syrian mukhabarat (secret police) prison were buried on the hill."
The prison dates back to 1976, when Syrian troops first moved into Lebanon a year after the outbreak of its 15-year-long civil war. It was used as a transit point through which Lebanese detainees on their way to Syrian jails passed.
Syria withdrew its forces from Lebanon under intense domestic and international pressure following the assassination two months earlier of former Lebanese prime minister Rafiq al-Hariri. Syria has strongly denied any involvement in the killing, which is under investigation by a UN panel.
Human rights abuses
Amnesty International said that during and after the war "mass human-rights abuses were committed with impunity - including killings of civilians, abductions and 'disappearances' of Lebanese, Palestinian and foreign nationals, and arbitrary detentions - by various armed militias and Syrian and Israeli forces".
Lebanese MP Akram Shuhayeb, an ally of anti-Syrian Druze leader Walid Jumblatt, pointed the finger at Syria for the Anjar deaths.
"The responsibility for this mass grave lies with those who held sway" in the area, a thinly veiled reference to Damascus.
Lebanon's ruling parliamentary faction, the Future Current movement of Saad al-Hariri, accused Syria of putting up a smokescreen over the graves.
Syria has suggested the bodies could be those of people killed in intra-Lebanese or intra-Palestinian clashes at the beginning of the civil war, before Syrian forces entered the country.