"We want peace with justice. Any truce offer is only as good as the principle and sincerity behind it... An enduring peace under the rule of law is what we aspire for," Mrs. Arroyo said.
She said the MILF must show that its unilateral ceasefire "is not a tactical ruse."
The Department of Justice (DOJ) also announced it will press on with the criminal charges against MILF chairman Hashim Salamat and his henchmen despite the rebel groups declaration of a unilateral 10-day ceasefire effective June 2.
Justice Undersecretary Jose Calida said the MILF declaration of ceasefire will not affect the judicial process.
"In other words if there is combat in a particular area, the ceasefire will give a rest period or respite between the two combatants but it does not in anyway affect the criminal cases that we have filed," Calida said.
Calida said it would be better for the MILF leaders and members to come out and answer the charges lodged against them.
"The proper procedure is for them to come out and file their counter-affidavit, there will be a formal preliminary investigation," he said.
In a statement, Mrs. Arroyo reiterated the governments three conditions which the MILF must comply with before the unilateral truce offer can be considered.
Mrs. Arroyo mentioned her earlier demand that the MILF should "unequivocally and unambiguously" renounce terrorism and their links with international terrorist organizations and surrender those responsible behind the attacks.
The President also said the MILF should "reveal where its units are located so that we can clearly (see) that these units are not in any way merged or coalesced with any terrorist or criminal groups that are outside of the purview of peace process."
The government has put up a P5-million reward for the capture of Salamat and three of his henchmen Ghadzali Jaafar, vice chairman for political affairs; Al Haj Murad, vice chairman for military affairs, and spokesman Eid Kabalu.
Warrants of arrest have been issued for their arrest after authorities tagged them responsible for the bombing of the Davao airport and Sasa wharf that left 38 people dead in March and April.
The MILF has been blamed for the spate of bomb attacks on civilian targets, among them the recent attacks in Maigo and Kolambugan towns in Lanao del Norte, as well as the raid on Siocon town in Zamboanga del Norte and the bombing of a market in Koronadal City in South Cotabato.
Following the Siocon attack, Mrs. Arroyo called off the peace negotiations with the MILF in Kuala Lumpur, Malaysia and ordered the military to launch "punitive actions" against the separatist guerrillas.
She also gave the MILF until June 1 to cease retaliatory attacks or face the consequence of being branded as a terrorist organization.
On Wednesday, the MILF declared a 10-day unilateral ceasefire and expressed hope Mrs. Arroyo would immediately halt the military offensive against them.
"Peace does not simply means the silencing of the guns. It means the willingness of both sides to safeguard and to serve the people in their communities and to come together under a common sovereignty and Constitution," Mrs. Arroyo said.
The attack came a day after the MILF declared a 10-day unilateral ceasefire.
Reyes said the government is not in a position to withdraw the warrants of arrest.
"Its a judicial process of the law. We cannot stop the judicial process. What would we say to the widows and the orphans of those killed in these bombings? Somebody has to account for those crimes," he said.
Reyes stressed the government has not closed the door to peace negotiations.
Bunye, for his part, said the government will guarantee the safety and due process of the rebel leaders and those responsible for the attacks if they surrender.
The MILF, through Kabalu, has demanded the government should pull out from captured MILF camps and recall the warrants of arrest issued for them.
He said Mrs. Arroyos demand for the rebels to renounce terrorism was "impossible." "We cannot renounce something we are not engaged in," Kabalu said.
He also said the MILF could not turn over fighters involved in "legitimate encounters" with the military.
In a joint statement by the MILF and the Bangsamoro civil society, they urged the military to "respect the unilateral ceasefire declared by the MILF and they (government and military) must show sincerity."
The Catholic Bishops Conference of the Philippines (CBCP) separately appealed to the government and the MILF to jointly facilitate the return of evacuees to areas affected by recent hostilities during the duration of the 10-day unilateral ceasefire.
Also, Ismael Abubakar Jr., the newly installed Speaker of the Regional Legislative Assembly in the Autonomous Region in Muslim Mindanao (ARMM), said they would pass a resolution appealing to Mrs. Arroyo to immediately work out the resumption of the peace talks.
Surigao del Sur Rep. Prospero Pichay, chairman of the House defense committee, said the MILF must show sincerity first.
"I hope this time they will be sincere. We already have five interim agreements. We can only wait and see if this new initiative is backed by sincerity," he said.
Pichay said Mrs. Arroyos policy of punitive action against the rebels "has been vindicated."
Foreign Affairs Secretary Blas Ople said he had already informed the Organization of Islamic Conference (OIC) in Tehran of the MILF ceasefire declaration and a permanent ceasefire offer of the government but said "their (MILF) sincerity is still subject to proof."
"If the MILF leaders prove sincere, they will be rewarded with a just and generous peace," Ople said. "The OIC foreign ministers welcomed the reported declaration of the MILF of a unilateral ceasefire and President Arroyos sympathetic response." With Aurea Calica, John Unson, Lino de la Cruz