ROME, Nov 12 (Reuters) - More than 1,800 Italian schools received hoax bomb warnings on Thursday but many ​opted to remain open, following new advice from the government for handling such security threats.

Prime Minister Giorgia ‌Meloni's government said public buildings should be cleared only if there is concrete evidence of danger after a wave of fake bomb alerts on Wednesday triggered school closures across Italy.

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On Thursday, 1,803 schools received threats and some were evacuated, although hundreds opted to ignore the warnings or quickly ​reopen following the new guidance.

The alarm had been more widespread on Wednesday, when 6,300 schools were affected and ​panic spread among parents.

These were the latest in a series of hoaxes and cyberattacks that ⁠have recently also targeted supermarkets, blood banks, air traffic systems and broadcasters across Europe.

As the alarm spread for a ​second day, Meloni summoned opposition leaders to her office for talks on how to handle similar incidents and announced plans for ​a protocol aimed at limiting their impact.

"Buildings should not be evacuated in the absence of concrete elements beyond the mere receipt of a mass email that would suggest a genuine danger exists," the prime minister's office said.

The warnings on Thursday were again signed by "Mikhail Andropov" and included another threat to the ​prime minister, who was also targeted on Wednesday.

Some European officials suspect Russia may be behind a campaign of disruption to everyday life ​in European nations supporting Ukraine after Moscow's invasion.

Italian officials have so far said there was no evidence of that. Russia denies involvement and ‌accuses the ⁠West of a smear campaign.

Russia's ambassador to Italy said on Thursday that the Russian authorities were ready to help their Italian counterparts to track down whoever was behind the threats.

'GOOD ANTIVIRUS'

After the two-hour meeting, opposition leaders from the centre and left said it was up to the government to come forward with proposals to address such threats, but criticised Meloni for what they ​described as inadequate investment in ​cybersecurity.

"How has the money been ⁠spent so far? Yesterday's alarm could have been dealt with using a good antivirus programme," said former Prime Minister Matteo Renzi, leader of the centrist Italia Viva party.

Authorities in Scotland, Northern ​Ireland and the Republic of Ireland said many schools had received similar threatening emails from ​abroad, but classified ⁠them as hoaxes and allowed classes to continue.

"We asked the prime minister why, in Ireland, authorities had warned schools in advance and told them to remain open because the emails were not considered a threat," said Nicola Fratoianni of the Green-Left Alliance.

Opposition parties have ⁠accused Meloni ​of prioritising spending on conventional military equipment while neglecting what they say are ​more pressing cyber threats.

"We need stronger coordination among the bodies responsible for cybersecurity, and we have proposed shifting part of the available resources towards cyber defences," ​said Elly Schlein, the leader of the main opposition Democratic Party.

Additional reporting by Alvise Armellini and Marco Roberti Editing by Keith Weir