Franjiyah said on Thursday that he disagreed with Lahud on the Maronites' representation in government.
"I will certainly not enter another government during the term of President Emile Lahud. Every experience I've had with the president has led me to disappointment," Franjiyah said.
He added that he and the armed Shia group Hizb Allah were deceived during consultations on government formation by Lahud, outgoing Prime Minister Umar Karami and Parliament Speaker Nabih Birri.
Franjiyah held the three responsible failing to establish a new government.
The crisis could delay May elections, though Lahud will consult with legislators on Friday on naming a prime minister-designate to keep alive hopes that a government could be formed quickly to supervise the poll.
"I am for holding elections. It's not that important if we win or lose," Franjiyah said.
Franjiyah: We might arrive at a
situation leading to violence
"If we don't reach the stage of an election that would reflect the public's will, then we might arrive at a situation that would lead to violence."
Franjiyah suggested that member of parliament and former minister of public works Najib Miqati be asked to form a new government.
Karami failed on Wednesday to form a government, saying his attempt had hit a wall.
His second failure to form a government since protests over the 14 February assassination of former prime minister Rafiq al-Hariri may lead to the postponement of legislative elections scheduled for May.
The Lebanese parliament's four-year term ends on 31 May.
The constitution requires polls be called at least a month before voting day.
"I will certainly not enter another government during the term of President Emile Lahud"
Outgoing Lebanese Interior Minister Sulayman Franjiyah
If elections are not held in May, parliament, currently dominated by pro-Syrian legislators, can extend its term by several months to avoid a political vacuum.
Lebanese Democratic Alliance leader Antoine Andrawos, in an interview with Aljazeera, said the opposition was scheduled to meet on Thursday evening to decide its course of action.
"We stick to our position that by virtue of the majority they enjoy in parliament, the pro-government parties should form the new government," he said.
The opposition supports the creation of a government headed by an impartial prime minister, with ministers who will not be nominated as candidates for the parliamentary elections, Andrawos said.
"We have ministers who have not been nominated, notably Laila al-Sulh, Rashid al-Sulh and Adnan Qassar. Such people could head the new government and in turn they could select trustworthy, impartial ministers," he said.
The opposition may again take to
the streets if polls are postponed
"Our duty is to help ease the crisis and we might take a decision today to name some candidates. But we hold the Lebanese president accountable as he is responsible for defending the constitution and has to resolve the crisis."
The opposition politician blamed the government for procrastinating for the past 50 days.
Asked if it was still feasible to hold elections as scheduled,
Andrawos said: "Yes, surely. As we see it, the government should hold the elections on the basis of the year 2000 law."
Replying to the question on whether the opposition had a deadline for government formation, Andrawos said: "If parliament extends its term of duty beyond 29 April, we will rally in the streets and ask the Lebanese people and their representatives to join us.
"We will then organise a procession to the president's office and demand the holding of elections on time. And we will stick to this demand."