Roth said he doesn't want to discuss the constitutional situation, but "we hope that there will be a stable, pro-European government in Italy without delay".
Italy, the EU's fourth-biggest economy, has been without a government since elections in March because no political group can form a majority.
Mr Mattarella's veto on Sunday enraged both League leader Matteo Salvini and Five Star Movement leader Luigi Di Maio, who threatened to start impeachment proceedings against him. Although mainly ceremonial, the president does have the power to appoint heads of government and dissolve parliament.
"It's an institutional clash without precedent", he said on a live-streamed Facebook video.
Financial markets have been reassured, at least for now, by Mattarella's move.
While vowing to press Brussels to respond to the concerns of Italians, Cottarelli said any such dialogue must be in "full recognition that as a founding country of the European Union, our role in the union is essential, as is our continued participation in the eurozone".
The euro's surge meant that the dollar pulled back from a six-month peak of 94.30 hit against a basket of rivals on Friday.
However, analysts believe the respite could be temporary.
He also has emphasized the need to bring down Italy's enormous debt load, which costs about 60 billion euros ($70 billion) a year to service through interest payments, in order to free Italy from market forces.
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The country could be headed for another election in coming months.
"We don't think this rally can be sustained".
A boost for the populists?
ROME-Italy's president asked a former International Monetary Fund official to try to form a new government, in a closely watched meeting hours after he blocked the formation of a government supported by two euroskeptic, anti-establishment parties.
"I asked for the (economy) ministry an authoritative person from the parliamentary majority who is consistent with the government programme. who isn't seen as a supporter of a line that could probably, or even inevitably, provoke Italy's exit from the euro", Mattarella said. But with new elections all-but certain and the anti-euro League gaining support, polls suggest the populists can only benefit from the chaos - raising the threat of more market turbulence ahead.
A source from Five Star told Reuters the party could campaign with the League in a fresh vote. The political mainstream is widely blamed by Italians for a sluggish economy, high unemployment and rising poverty - not to mention the migration crisis of recent years.
"I have given up my mandate to form the government of change", said Conte to reporters after leaving failed talks with President Sergio Mattarella.
While he had approved all their other ministerial picks, Mr Mattarella said he had the right to block nominations that could harm the country.
Mattarella's power play will nearly certainly work to the favor of the populist leaders because it will galvanize voters into reasserting with even greater force their sovereignty.