"Time is running out," Dayri told AFP in an interview on Tuesday. "Terrorism amounts to a danger not just for Libya and its neighbours. It is an intensifying threat to Europe.
"Without a political solution, the country could get trapped in a full-blown civil war like in Syria," he said.
The North African country has collapsed into a bitter struggle between rival governments and militias since dictator Moamer Khadafi was overthrown and killed with Western help in 2011.
Two parliaments compete for legitimacy in different parts of the country. Islamist militants control the capital Tripoli, while an internationally-recognised government has been relegated to the eastern city of Tobruk.
- 'No convincing response' -
There are also fears that the conflict is attracting an increasing amount of foreign jihadists, and a number of attacks have been claimed by the Islamic State group.
The minister, a member of the Tobruk government, underlined that his government is not asking for a new Western military intervention as in 2011, but only for "the reinforcement of the Libyan army's capabilities".
"The creation of a national unity government is a priority for Libya, not just an international demand," said Dayri. "But even if we achieved that tomorrow, we would still need help with our army.
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"Yet I have had no convincing response from the United States or Europe."
He appealed to the UN Security Council last week to remove the arms embargo that has been in place since 2011, but the request has met with resistance, particularly from Russia, over concerns the weapons may end up in the wrong hands.
The international community has been pushing for a diplomatic solution, but is increasingly concerned that Libya is turning into a chaotic zone that can be exploited by jihadist groups.
The threat is heightened by Libya's proximity to Italy, and its use as a launchpad for thousands of migrants trying to reach Europe by boat.
Libya's army and police are deeply divided and weakened after decades of subservience to the dictatorship and the more recent collapse of the state.
Dayri remains adamant that his government's forces, led by controversial general Khalifa Haftar, represent the seed of a national army.
But their rivals in Tripoli are deeply hostile to Haftar for his fiercely anti-Islamist views, and his expected appointment to the new post of "commander-in-chief of the army" risks worsening the divide at a time when negotiations are making scant progress.
Another round of UN-brokered talks was due in Morocco on Thursday, but the Tobruk government pulled out following suicide bombings claimed by the Islamic State group in the eastern town of Al-Qoba on Friday that left more than 40 dead.
The Tobruk government was angry with its rival in Tripoli for "not condemning terrorism strongly enough", Dayri said, though he made clear his government would return to the talks, without specifying a date.
"Our essential condition for forming a government of national unity is that all sides engage in combatting terrorism," he said.