"We believe the government will use all diplomatic channels to bring back the culprits to India so that they can be tried as per the Indian law," party spokesperson P C Chacko told reporters.
He said the Congress fully supports the "bold" initiative taken by Prime Minister Manmohan Singh.
A party leader speaking on the condition of anonymity, however, said the demand for "arrest" of Italian ambassador Daniele Mancini is not logical but there is a possibility of declaring him a "persona non grata" after which he will have to leave the country, in case Italy does not agree to send back the two accused.
Earlier in the day, the apex court restrained Mancini from leaving the country without its permission, taking exception to his government's refusal to send back the duo.
Massimiliano Lattore and Salvatore Girone were charged with homicide for killing two fishermen off the Kerala coast in February last year in an anti-piracy operation. They were permitted by the apex court on February 22 to go to Italy for four weeks for voting in elections and directed to return within four weeks.