During the meeting at the Kremlin, Mattarella told Putin that the countries need "greater collaboration and coordination against terrorism".
The Italian president was the first foreign leader to meet Putin after the St Petersburg metro bombing which killed 13, and restated Italy's condolences for the attack.
Putin said that Italy was a "reliable partner" of Russia's and described his conversation with Mattarella as "frank and concrete", but added that relations between the two countries were "not at their maximum".
The Russian leader added that improving the trade relationship between Russia and the European Union would be "in the common interest".
Following their meeting, the pair held a joint press conference in which Putin warned he expected further chemical attacks by rebels in Syria. Putin has been quick to blame the attacks on rebels rather than the Assad regime which he supports, though the investigation into who is responsible is still ongoing.
Mattarella said he hoped that Russia would use its influence in the country to avoid future attacks of this nature.
The meeting took place as G7 ministers met in Italy to discuss issues including the ongoing crisis in Syria. However, Italy's foreign minister Angelino Alfano said on Monday that "no consensus had been reached" on sanctions on Syria. The US has said it will impose additional sanctions, but the other countries in the group had "different opinions" on the possibility, with Italy expressing reservations as to their utility.
The United States launched missile strikes on a Syrian air base in response to the suspected chemical attack, and US Secretary of State Rex Tillerson has accused Russia of "failing to uphold the agreements that stipulated Russia [...] would locate, secure and destroy all chemical weapons in Syria".
Tillerson, who is also in Moscow to meet his Russian counterpart Sergei Lavrov, said it was "unclear whether Russia failed to take this obligation seriously" or had "been simply incompetent".
Italy and Russia
In December, Prime Minister Paolo Gentolini said Italy's relationship with Russia would be defined by events in Syria, but the Mediterranean nation has been one of Russia's strongest allies over recent years.
The countries have strong trade links and Rome notably aired reservations about the utility of sanctions imposed over the Kremlin's conduct in Ukraine. Italy has stalled the extension of these sanctions - although it has never broken ranks from the common EU position.
And as well as support from the ruling Democratic Party, Putin also enjoys close links with all three of Italy's major opposition parties, particularly Forza Italia, having struck up a bond with Silvio Berlusconi during his stints in power.
The leader of the far-right Northern League Matteo Salvini meanwhile has spoken positively about Russia for years, calling for an end to sanctions, and has travelled to Moscow on multiple occasions, meeting Vladimir Putin in 2014. Earlier this year, he met with Russia's foreign minister, Sergey Lavrov, and signed a deal with Putin's party.
And the anti-establishment Five Star Movement party has also come out in support of Putin, though it has also faced accusations of links to a network of pro-Russia fake news sites.
A BuzzFeed News investigation in late November showed that leader Beppe Grillo's blog, the party's official websites, and several supposedly independent pro-Kremlin news sites all shared IP addresses. Grillo vehemently denied the claims, without providing an explanation for the findings.