Luca Ceriscioli said quakes and snow had caused landslides and thousands of families were suffering power cuts, with some villages left isolated.
A man was killed and another reported missing in the nearby Abruzzo region.
European Commission President Jean-Claude Juncker vowed EU solidarity with Italy after the tremors.
Marche was one of the regions worst hit by the earthquake of 24 August, with 46 of its 298 victims losing their lives in a single mountain village there, Pescara del Tronto.
The Lazio region was also affected on Wednesday and the tremors were felt in the capital, Rome.
Amatrice, the Lazio town where 236 of the August deaths were recorded, is close to the epicentre of the new quakes.
The tremors came after some 36 hours of steady snowfall in mountainous areas around Amatrice and Norcia.
In Teramo, Abruzzo, a man of 83 was found dead in the rubble of his barn which had collapsed, while in Ortolano, also in Abruzzo, a man was swept away by an avalanche, Italy's Ansa news agency reports.
The Italian Institute of Geophysics and Volcanology said it had recorded "some 200" tremors above magnitude 2 on Wednesday in Abruzzo and Lazio.
The first big quake struck at 10:25 (09:25 GMT) with a magnitude of around 5.3, followed at 11:14 with one of 5.4, followed some 11 minutes later by another of 5.3, the institute said (in Italian).
At 14:33, a fourth quake measuring 5.1 occurred, the institute says.
The first three were around 9km (5.6 miles) in depth, meaning they were dangerously close to the surface, while the fourth was even shallower, at 6.9km deep, according to the US Geological Survey.
"It's a catastrophe," Mr Ceriscioli said, as civil defence leaders met to discuss the response in Marche.
"Today's tremors and the snow of the last days add huge problems, especially on the roads, to the dramatic situation caused by the [August] earthquake.
"The lack of electricity causes serious problems to thousands of families who don't know where to go or to stay."
The priority, he said, was "taking people to safe and warm places".
He appealed for "maximum mobilisation", saying the army was already lending assistance, and called on other parts of Italy to send help to clear the roads and restore power.
'People were screaming'
In the Abruzzo village of Montereale, south of Amatrice, farmer Nello Patrizi, 63, told AFP News agency: "It was an apocalyptic shock. We were petrified.
"The first [quake] was bad enough, the others seemed even stronger. You had the impression everything was collapsing, people were screaming. It was a terrible thing.
"With all the snow there was this morning, people could not get out of their houses. I thought 'all we need now is an earthquake' and here it is."
People were given shelter in a large tent erected on a sports ground in Montereale.
Saying the rest of Europe shared Italy's pain, Jean-Claude Juncker said he was sending his commissioner in charge of humanitarian affairs to Italy.
"We will provide all kinds of efforts, instruments, helps at our disposal because I think that in that matter, as in the migration matter, Italy cannot be left alone," he said.
"An earthquake in Italy is an earthquake in Europe - that's the way I'm considering this sad event."
Schools have been evacuated in the areas worst affected while in Rome, the underground system was shut as a safety precaution.