Italian Foreign Minister Gianfranco Fini said a separate Italian inquiry into Mr Calipari's death would continue.
She noted that centre-right parties had come on board - even the rightist Gianfranco Fini of the National Alliance.
One contender for the foreign minister's job is Gianfranco Fini, the leader of a once-fascist party and now deputy prime minister.
Mr Berlusconi's key partner, outgoing Foreign Minister Gianfranco Fini, said earlier on Friday that he expected the formation of a new cabinet very soon.
In Italy, Gianfranco Fini, who has distanced his party, the post-fascist National Alliance, from its fascist heritage, joined the government of Silvio Berlusconi in 1994.
Gianfranco Fini -- a former party ally -- lashed out, accusing him of a lack of attention to the economy and structural reforms that Italy needs.
But Gianfranco Fini, the post-fascist leader, is against referendums that could lead to reforms of hiring rules and pensions, though he wants a new electoral law.
Making things worse, a rebellion in mid-2010 by his former lieutenant, Gianfranco Fini, left the government with a thin and fluctuating majority in the Chamber of Deputies.
He had successfully fused his own party with that of the formerly neo-fascist Gianfranco Fini to create a single movement of the right, the People of Freedom (PdL).
That would not be easy if he were linked to old school, professional politicians such as Gianfranco Fini of the National Alliance or Pier Ferdinando Casini, a Christian Democrat.
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Both of Mr Berlusconi's senior lieutenants, Gianfranco Fini of the National Alliance and Pier Ferdinando Casini of the Union of Christian Democrats, have said as much in recent weeks.
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But he would be vulnerable to Gianfranco Fini, the foreign minister, who is also deputy prime minister and leader of the second-biggest party on the right, the formerly neo-fascist National Alliance.
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Gianfranco Fini, the post-fascists' leader, has not forgiven Mr Berlusconi, his supposed ally on the right, for sinking the constitutional reforms (along with Mr Fini's hopes for a directly elected president).
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And what parts remain for those actors on the right, Silvio Berlusconi, the leader of the opposition, Gianfranco Fini, head of the post-fascists, and Umberto Bossi, leader of the separatist Northern League?
His government's use of procedural devices to cut short parliamentary debate has even been criticised by his ally, Gianfranco Fini, former leader of the National Alliance and now speaker of the lower-house Chamber of Deputies.
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But others, including the post-fascist National Alliance's leader, Gianfranco Fini, whose party is set to join Mr Berlusconi's in a coalition government if the left loses the election due by next spring, suggested that the boss had mistackled.
The head of the Future and Freedom (FLI) party, Gianfranco Fini tweeted that the Monti coalition opened up a "prospect of renewal" while Christian Democrat leader Pierferdinando Casini said it was not so much "a personal party but a hope for Italians".
His one-time friend and now political enemy Gianfranco Fini called on him to resign at the weekend, saying "the government must understand that it is not credible, even if it wins in parliament by a vote, because with a majority of one vote you can survive but you can't govern".
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