The speech by Pellegrini, who had held the position of deputy prime minister before that, at the swearing-in ceremony was streamed live by the network broadcasters.
Later in the day, European Council President Donald Tusk sent a congratulatory letter to Pellegrini.
"On behalf of the European Council, I wish to convey my congratulations on your appointment as Prime Minister of the Slovak Republic and on the formation of your government," Tusk said, as quoted by the press service of the EU Council.
The Slovak authorities have been facing a political crisis since the murder of journalist Jan Kuciak. The journalist, who had been investigating the Italian mafia’s activities in Slovakia and its links to senior Slovak officials, was found dead with his fiancee in their home in a south-western Slovakian village in late February.
Pellegrini showed Kiska the first list of government candidates on Tuesday, but the president disagreed with some of the proposals, mainly with the candidate for the interior minister. On Wednesday, Pellegrini brought the president a new list, which was approved.