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8 year oldThe shares have been dragged down by fears that a rescue of the troubled Monte dei Paschi bank might fail.
The euro was hit after Mr Renzi said he would resign. At one stage it hit $1.0505, its lowest level against the dollar since March 2015.
But then it rebounded and by 1500 GMT was at $1.0724, a rise of 0.5%.
Trading in bank shares has been volatile. At the open Monte dei Paschi shares fell by more than 5%, then recovered to trade higher. But then they headed lower again, and by early afternoon were down 4%.
Trading in Unicredit shares, which was temporarily suspended when a circuit-breaker kicked in, are down by 3.45%; Banca Popolare di Milano and Banco Popolare Societa Cooperativa are both more than 7% lower.
Poll defeat risks Italy political crisis
Referendum adds to Italian banks' woes
Analysts are particularly concerned about Italy's banking industry, which is seen as vulnerable to a loss of confidence.
Many banks are struggling with a burden of bad debt and are in need of refinancing.
That finance is likely to be harder to come by amid a political crisis. It was thought that a victory for the Yes camp in the referendum could have seen investors stepping in to help recapitalise the banks. But given that the No voters won, analysts are now unsure what help will be forthcoming
"The economy is gradually recovering but it is also being held back by the problems in the banking sector which haven't been addressed properly so far," said Lorenzo Codogno, former chief economist at the Italian Treasury and founder of LC Macro Advisors.
"So I think the combination of domestic and international factors plus the open issue of the banking sector are at the root of not particularly brilliant growth."
Kathleen Brooks, research director at City Index Direct, said there was caution among investors but not panic.
"While the markets are likely to remain nervous as we start a new week, they haven't fallen off a cliff, so far," she said.
"Either markets are becoming immune to political risk, or they are taking the view that the Italian issue will be a slow-burner, even if the president can't form a government, he still has 70 days to try, and that seems quite far away at this stage."
If the consortium of investors does decide the plan to rescue Monte dei Paschi is now too risky then the government may have no choice but to nationalise the bank.
That would trigger a so called "bail in" which means people who lent the bank money would have to write it off.
Unfortunately, 65% of those creditors are ordinary retail investors so the damage would be widespread and politically toxic.
However, the Italian economy is in a fragile state and a period of political uncertainty could do it further damage.
The size of Italy's government debt is also a concern. Government borrowing, depending on which figures you look at, is one of the largest in the eurozone.
Italy's cost of borrowing rose on Monday. The country's 10-year government bond yield was up from 1.896% at the end of last week to 2.034%. Yields rise when the price of bonds fall.
Mr Renzi's defeat adds to pressure on the European Union following June's Brexit vote in the UK.
"It's not very hard to see a new election on the horizon, and it's not very hard to see the 5-Star Movement taking power with stated aims to either leave the EU, drop the euro, or both," said Mark Wills from State Street Global Advisors.
"For Italy, establishing stable governance and a plan to guide the nation is of critical importance given the fragility of the economy, challenging policies and the liquidity problems in the banking system."
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