The debate was prompted by multiple trips to Syria, Crimea, and Azerbaijan where the MEPs' opinion may have been passed off as the official stance of the European Parliament.
David McAllister, a member of the European Parliament Committee on Foreign Affairs has sent a letter asking the European Parliament to tighten controls over the European lawmakers' foreign visits.
He suggests introducing sanctions against members who offer opinions diverging from that of the parliament.
"If they want to make the requirements more strict, let them. But they can't keep us from going anywhere," said Estonian MEP Yana Toom of the ruling Center Party.
In 2016 Toom, together with Latvian MEP Andrejs Mamikins of the Harmony party, visited Syrian dictator Bashar al-Assad and his Russia-backed regime alongside Russian officials.
"Our employer is not Antonio Tajani or other honored colleague but rather our voter. And they're the ones we have to answer to," said Toom.
"I always say that it's my personal opinion. I represent neither the parliament, nor the Liberal Democrats group or the Center Party for that matter. I am here on my own and represent my voters. It's likely that not all of them, for that matter," said Toom.
Mamikins too says he's proud to have visited Bashar al-Assad, whose regime is believed to have used chemical gas against a rebel-held village this year, killing over 80 people.
"It was worth going there as it's always useful to talk. It's better to communicate and to talk, not just condemn and talk with resolutions sitting in warm offices here at the European Parliament," said Mamikins.
Mamikins' visits have been condemned by Latvian Foreign Minister Edgars Rinkevics.
Tatjana Ždanoka, another Latvian MEP, has also visited Bashar al-Assad in Syria.
However not just MEPs but receiving countries too can cause problems, suggests Sandra Kalniete, an European Parliament member of Latvia's ruling Unity party.
"[In these countries] people at the reins of power want to pass off the parliamentarians' views as the official position of the European Parliament. Most people, in Latvia too, don't realize where's the limit," she said.