Speaking in an interview in Strasbourg on Monday, Metsola said Europe's moderate, pro-European parties needed to offer an "alternative" to voters.
"I'm worried that if we don't - as part of the pro-European, constructive (...) majority at the centre - appeal to our voters, then our voters will feel that they have no choice, that they have to retreat to the fringes, to those people who want to destroy rather than to build," Metsola explained, referring to the eurosceptic far-right.
Current polls predict a surge in support for far-right parties in the European elections, which take place across the continent on 6-9 June.
It follows far-right leader Geert Wilders' surprise electoral victory in November's Dutch election, and comes as far-right parties including Germany's Alternative für Deutschland and France's Rassemblement National make historic gains in national polls.
But projections also suggest that the European Parliament's current ruling coalition of social democrats, conservatives and liberals - who work together to ensure EU legislation can be passed - will cling on to its majority.
Metsola, who belongs to the centre-right European People's Party (EPP) and who took over the presidency of the European Parliament in January 2022, said that by finding solutions to challenges such as the COVID-19 pandemic and Russia's invasion of Ukraine, the coalition had proved its resilience.
"These are big challenges that we have overcome and that we continue to show unity over, and I think that's where we would find that unity in that centre," Metsola explained.
"So I think we can provide an alternative. We can counter that (far-right) threat if we want to call it a threat, and I'm confident we can do so," she added.
Next five years 'will not be any easier'
But Metsola also warned that the European Parliament's next five-year term "will not be any easier" than the previous one.
Since the 2019 European elections, the 27-country bloc has faced a raft of unforeseen challenges, including the COVID-19 pandemic, Russia's invasion of Ukraine and a looming economic crisis.
The 720-seat European Parliament, the bloc's only democratically-elected institution has also been rocked by the so-called 'Qatargate' cash-for-influence scandal.
In December 2022, the parliament's vice-president Eva Kaili and other senior parliamentary figures were accused of accepting hundreds of thousands of euros for influencing EU decisions to the benefit of Qatari and Moroccan officials. All vehemently deny the allegations.
Suspects were predominantly social democrats, threatening to stain the centre-left group's reputation.
The scandal also sent shockwaves across Brussels and forced parliament to clamp down on lax rules on staff conduct. The European Ombudsman has nonetheless questioned whether the reforms introduced under Metsola's initiative are sufficient to restore voter confidence.
Asked whether she feared the scandal had eroded trust in the European Parliament, Metsola urged voters to judge the parliament on its response to the sprawling graft case.
"We took the immediate decision to introduce measures to make sure that we saw where the gaps were, to insert firewalls and to make sure alarm bells are sounded earlier," Metsola explained, reassuring that rules "are observed" in the parliament.
"We have done a lot of work in the past year, and I would like us to be judged on that, rather than the (...) allegations with regards to a small number of individuals," she added.
Asked whether some far-right parties could choose to join a new European coalition, Metsola refused to speculate on the formulation of the future parliament, assuring that the current parliament has "found unprecedented unity in the centre."
There is speculation that the European People's Party (EPP) - the parliament's biggest political group at the centre-right - could be open to an alliance with Italian premier Giorgia Meloni's far-right Fratelli d'Italia party.
EPP Chairman Manfred Weber met with Meloni last year to discuss a potential collaboration at the EU year, although the prospect has been dismissed by other prominent figures from Europe's centre-right.
"Let's look at what we have done in that centre, that pro-European centre," Metsola said.
"It is that that we need to build on, and I look forward to be able to continue to do that from 2024 to 2029."