The opposition met the prime minister on Monday and reiterated their demands for holding the elections on time, dismissing the security chiefs and the right to veto the nominations of the interior and justice ministers.
But Aljazeera's correspondent in Beirut reported that some opposition members felt that Miqati was less than enthusiastic in conceding to their demands.
"We in the opposition will seriously review this matter. If we find that he seemed persistent to go along with this attitude, we might probably withhold our vote of confidence to this new prime minister," opposition lawmaker Walid Eidu said.
But some other opposition members called for patience, saying they would support any initiative that would facilitate the holding of parliamentary elections.
Al-Hariri's sister Bahia met
President Lahud to back Miqati
"We are concerned with the formation of the new government to avoid a political vacuum. We have no demands or stipulations. All these issues, including the elections and their timing could be resolved in the parliament," outgoing deputy speaker Michel al-Mur said.
Some political groups, however, saw the parleys between the government and the opposition as a cleverly crafted deal to obstruct planned elections in May.
Miqati's appointment on Friday came after his pro-Syrian predecessor Umar Karami resigned twice in six weeks, leaving the country without a government as it confronted its deepest political crisis since the end of the 1975-1990 civil war.
US President George Bush, meanwhile, issued a stern reminder to Syria, the main power broker in Lebanon for almost three decades, to complete its troop pullout from the country before the elections.
Bush said: "When I say, get out of Lebanon, I mean out of Lebanon with all your troops and all your security services and all the people trying to influence that government.
Bush has said he wants Syrian
influence in Lebanon to end
"It is in the world's interest that Lebanon be allowed to have free elections, because a free society will help spread the peace."
Lebanon has been without a government since Karami resigned at the end of February under the weight of huge protests sparked by the assassination of his predecessor Rafiq al-Hariri in a massive Beirut bomb blast.
In the upheaval that followed, the international community succeeded in pushing Syria to promise an end to its 29-year military presence in Lebanon by 30 April, although it remains a powerful political influence.
Miqati, a family friend of Syrian President Bashar al-Asad, met former prime ministers on Saturday and started parliamentary consultations on Monday, facing an end of April deadline to call elections.
"We are concerned with the formation of the new government to avoid a political vacuum. We have no demands or stipulations. All these issues, including the elections and their timing could be resolved in the parliament"
Outgoing deputy speaker
"I come with an open hand and an open heart so that we can all cooperate in the interests of Lebanon," the 49-year-old Sunni Muslim said after his selection.
"We are facing a new period, a return to democracy," he said, pledging to be a symbol of moderation and national unity.
Lebanon's opposition, which found a powerful new voice after the killing of al-Hariri, blamed the attack on the pro-Syrian government and its supporters in Damascus and had been demanding the sacking of top security officials.
Miqati was chosen over Damascus protege President Emile Lahud's candidate, outgoing Defence Minister Abd al-Rahim Murad, amid signs of cracks among loyalists allied to Syria.
Al-Hariri's sister, MP Bahia al-Hariri, met Lahud for the first time since her brother's killing to back Miqati's nomination.
"We were facing two things: either to enter a constitutional vacuum or offer a compromise, and this is what the opposition chose," she said.
The opposition, which expects to win the elections and had warned of more mass street protests if a government was not formed soon, decided to back Miqati after he pledged to meet some of their demands.
"The important thing is that he keeps the promises he made," opposition MP Nayla Muawad said.