The Mediterranean rescue mission will be extended until the end of November, the government has said.
Navy vessels have recovered over 6,000 migrants while assisting the Italian authorities with humanitarian search and rescue operations.
The LE Samuel Beckett will replace the LE Niamh at the end of September and will deploy until November 30, dependent on the demands and requirements arising, defence minister Simon Coveney said.
He added: "I believe that we should continue to support Italy in a practical manner as far as possible and the Italian authorities have indicated that ongoing support is welcome.
"While our role in the Mediterranean is making an impact in the short term in terms of saving lives, longer-term solutions to address the migrant crisis are needed."
Last month the LE Niamh rescued 125 people from a large inflatable rib some 70 miles north-west of Tripoli.
Earlier, the ship's crew saved 367 people from drowning after a fishing vessel with some 600 people on board capsized north-west of Tripoli. The ship brought the rescued and 25 bodies to Sicily.
Mr Coveney said he will be meeting EU colleagues tomorrow in Luxembourg to discuss a range of issues including progress on the EU military mission in the Mediterranean (EUNAVFOR MED).
"A comprehensive approach is required to address this complex crisis with a view to developing longer-term solutions," he said.
The European Union has announced emergency talks on September 14 to deal with the worsening migration crisis.
Austria is increasing checks on lorries near its eastern borders following the discovery of 71 dead migrants in a lorry near the border with Hungary.