The deal that halted 13 months of conflict between Israel and Lebanon's Hezbollah movement is largely based on the implementation of UN Resolution 1701, which ended their last war in 2006.
It stated that Lebanese troops and UN peacekeepers should be the only forces in the south, where Hezbollah exerts control, and also calls for Israeli troops to withdraw from Lebanese territory.
Mikati said his cabinet had decided to "strengthen the deployment of the army and security forces in the South Litani region", in their first meeting following the ceasefire.
"I demand that the Israeli enemy abide by the ceasefire deal and withdraw" from Lebanese territory, he said.
"I hope this will be a new page for Lebanon, I hope the coming days will lead to the election of a president."
Bickering between Hezbollah and its political adversaries has left Lebanon without a head of state for more than two years.
Earlier, Lebanon's powerful parliament speaker Nabih Berri called on those displaced by war with to return home as the ceasefire took hold, also calling for the quick election of a president who can unite the country.
"I invite you to return to your homes... return to your land," said Berri, despite warnings to the contrary from Lebanon and Israel's militaries.
Berri heads the Amal movement and has led ceasefire talks on behalf of ally Hezbollah.
After nearly a year of limited cross-border fire initiated by Hezbollah over the Gaza war, Israel ramped up its aerial bombing of Lebanon on September 23, mainly hitting Hezbollah strongholds.
It later sent ground troops across the southern border.
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