Slovenia and Italy have already signed a memorandum of understanding and plan to sign a dedicated intergovernmental agreement in early December detailing the deployment plan, Defence Minister Roman Jakič told the MPs.
A total of 41 troops will take part in the mission, a crew of 33-35 aboard the Triglav and the rest at mission headquarters in Augusta.
The Triglav will patrol the waters east of Sicily. It is expected to set sail on 13 December, said the Chief of the Defence Staff, General Dobran Božič.
The MPs expressed cross-partisan support, arguing that refugees were a European issue and the deployment a sign of solidarity and humanitarianism.
There were questions regarding whether the Triglav is equipped to take refugees on board, but the minister said it was fitted out to provide first aid to refugees.
The mission, planned to last through the end of January, is estimated to cost half a million euros, but it costs about EUR 180,000 for the ship to lie idle in that period, according to Jakič.
The Triglav is a Svetlyak-class patrol boat which Slovenia got from Russia in 2010 as an offset for Soviet-era debt. It is 49 metres long, 9.2 metres wide and has a top speed of 27 knots.