Napolitano will hold talks with party and parliamentary leaders about the country's political future from Thursday, a presidential spokesman said.
He is hoping to avoid the need for new elections well ahead of the scheduled vote in 2011.
Prodi's diverse coalition has been squabbling since he took office only nine months ago.
Recently left-wing members of the government have voiced growing criticism of Prodi's backing for Italy's traditional pro-U.S. policies.
Wednesday's vote was seen as the culmination of that backlash, with Green and Communist members of the coalition voicing their objections by rejecting Prodi's entire foreign policy platform.
Simono Poidomani, an Italian journalist, told Al Jazeera:"I think in that case [forming a new government] Prodi will remain in control, but what could happen is the majority is likely to change - meaning new parties would come into the coalition government."
She said there might instead be a vote of confidence, in which case "this government may very well stay in charge".
The government needed 160 votes to win backing from the upper house for its foreign policy programme.
It received 158 votes; 136 members of the conservative opposition voted against it, and 24 abstentions - equivalent to a "no" vote in the Senate - caused the government to lose.
Although there was no constitutional requirement for Prodi to step down, Massimo D'Alema, the foreign minister, had said before the vote that the government should resign if it did not command majority support on foreign policy.
The government has been forced onto the defensive over its deployment of 2,000 troops in Afghanistan and the enlargement of a US military base at Vicenza in northern Italy.
On Saturday more than 80,000 people took part in a rally in Vicenza against the base expansion, including some senior coalition members.
Prodi had expressly forbidden members of his cabinet from joining the march.
D'Alema said that to go back on the approval that the prime minister gave last month for the base enlargement would be a "hostile act" toward the United States.
Prodi's coalition narrowly beat Silvio Berlusconi's conservatives in a general election last year.
His fragile ruling coalition, which ranges from Catholics to communists, has only a one-seat majority in the senate but in the past had managed to win majority support despite divisions by calling confidence votes.