The blast caused up to $4.6 billion worth of physical damage and a blow to economic activity of up to $3.5 billion, according to a World Bank assessment.
Macron said Thursday that he, Merkel, and EU chief Charles Michel have had "several exchanges" with Russian President Vladimir Putin on the situation in Belarus.
There would be a first government whose mission would be to carry out urgent reforms," said the French diplomatic source familiar with Macron's thinking.
Macron wants to use Lebanon's desperate need for international reconstruction aid as leverage to persuade its factions to choose a new administration.
The objective today is to act quickly and effectively to coordinate our aid on the ground so that it goes as efficiently as possible to the Lebanese people.
Macron was speaking to reporters in Beirut, after his plane touched down at the start of an official visit following Tuesday's deadly warehouse explosion in the Lebanese capital.
The special allowance sought to compensate for the "additional hardship associated with night work" accompanied by increased demand for police on the ground, added the ministry.
Macron, who has criticised Turkey for months over Ankara's role in Libya, also said the EU should push for sanctions over those involved in the north african country's conflict.
Painful discussions resumed "with the possible hopes of a compromise. Nothing has been agreed yet, so I will remain extremely cautious", said Macron as he arrived to the talks.
His comments, in a television interview marking Bastille Day, came after he oversaw the traditional military ceremony that was drastically downsized because of the pandemic.
Together with Macron, Merkel sketched out the backbone of the 750 million-euro ($840-million) fund proposed by von der Leyen to bolster the bloc's economy.
Macron has in recent months pursued a policy of rapprochement with Russia, reaching out to Putin over key areas of disagreement such as Ukraine, in an approach that has discomforted some EU allies.
Macron said the country would not obscure elements of its history or dismantle statues of public figures who may have advocated racist views or policies.
The government had put the cost at 110 billion euros in April but has since had to make upward revisions to take account of falling tax revenue and extra spending, it said in its budget update.