The National Coalition Party, the right wing Finns Party, the Swedish People's Party and the Christian Democrats Party will take part in the talks. If they are successful, the cabinet would have 109 seats, giving it a slight majority in the 200-member parliament.
Orpo acknowledged at a press conference that the parties differ on many issues, but said he believes these differences can be overcome. A cabinet could be formed in early June.
Local commentators have said immigration and carbon neutrality will require the most negotiations. Meanwhile, Orpo noted that planning public spending in a way that will not hamper economic growth will be a challenge.
Finns chair Riikka Purra said there are major disagreements, but these can be negotiated. Purra said her party had not made any commitments on specific issues during the initial consultations.
In the April election, the National Coalition Party emerged as the largest party with 48 seats, followed by the Finns with 46 seats. The Social Democratic Party (SDP), the leading party in the current Finnish coalition chaired by Prime Minister Sanna Marin, won 43 seats.
Orpo said at the press conference that the views of the SDP were too far apart in the initial consultations for the party to participate in subsequent talks.
Social Democratic Party leader Sanna Marin said after Orpo's announcement that Finland will likely have a right-wing government. Marin said her party's views differed with Orpo's, especially on the essentials of the welfare state.
However, Finnish national broadcaster Yle said that if the talks about a right-wing government fail, the alternative of a conservative-social democratic cooperation will be raised.