"Italy is hardly the only country that does business with Moscow and that does not want Moscow to turn against it," said Giampiero Gramaglia, a columnist and spokesman for the Istituto Affari Internazionali think tank in Rome.
The La Repubblica daily struck a similar tone, saying: "Putin is going all out trying to seduce European partners. But Mogherini did not let herself be seduced."
The paper cited Italian foreign ministry officials saying that the accusation was "too fragile" and said Mogherini herself, who is on a visit to Israel and the Palestinian Territories, smiled when she was asked about it.
She reportedly told her aides that the controversy was a "manipulation" against Italy, La Repubblica said, pointing to her long-term political ties with the US Democratic Party to refute the accusation of being pro-Kremlin.
"Italy and Germany have both put the brake on sanctions, favouring a more gradual approach against Russia so as no to burn the possibility of a negotiated solution," it said.
After failing to obtain Mogherini's nomination during a special summit of EU leaders in Brussels on Wednesday, Renzi said the accusation of Italy's pro-Russia bias from some Central European member states "does not stand up".
Mogherini's staff were quoted by the Il Messaggero daily pointing out to reporters that the minister had travelled to Kiev before Moscow earlier this month in an attempt to mediate in the spiralling conflict in Ukraine.
The report also cited aides saying: "The relationship with Russia is strategic for all of Europe, including Ukraine".
The accusations centre on that visit to Moscow in which Mogherini took the opportunity of a meeting with Russian President Vladimir Putin to discuss the South Stream gas pipeline project for pumping Russian gas to Europe.
Italy and Russia have strong economic ties, particularly in the oil and gas sector, and former prime minister Silvio Berlusconi famously enjoyed friendly ties with Putin and has gone on frequent visits to his residence near Moscow.
In a post on her blog, Mogherini explained her position during a visit to Ukraine in February, shortly after being named foreign minister and before Ukraine's pro-Russian president Viktor Yanukovych was ousted.
In it she accused Putin's Russia of "reviving an attitude of regional hegemony and competition with the West".
But she added: "Perhaps it would be wise for neither the EU nor the US to fall into the trap of contrast, not to side with one or the other but to facilitate a way out of the violence and towards national reconstruction".
The Il Fatto Quotidiano daily, however, shared some of the concern about ties with Russia saying that Mogherini "has never changed course from the Rome-Moscow axis".
"The Americans know that while Italy's heart...has historically been with Washington, the wallet is in Moscow," it said.
The paper pointed out that Italy was slow to condemn Russia's creeping invasion of Crimea in March saying: "Federica got her timing wrong".
It said the minister had also made the "mistake" during her visit to Moscow of inviting Putin to the Asia-Europe meeting in Milan in October - a summit between EU member states and ASEAN partners held every two years.
Retracing the 41-year-old's political evolution from her youthful involvement with the Communist Party to her support for the centre-left, the paper said: "She has lived for tactics and it is tactics that have undermined her now".