In a joint statement from EPP president Joseph Daul and group chair Manfred Weber, following the group's delegation to Ukraine, the deputies declared, "Russia has to stop being part of the problem and start being part of the solution.
"Russia has a responsibility to stop arms, equipment and trained personnel from passing the frontier and to accept such border controls. This is a central point with regard to the sanctions," they stressed.
The pair continued, "We fully recognise Ukraine's right and obligation to uphold law and order on its own territory and defend its sovereignty and territorial integrity.
"This should go in parallel with efforts to put Ukraine through a much-needed reform and modernisation process, and with the ratification of the association agreement with the EU", they argued.
"Russia has to stop being part of the problem and start being part of the solution" - Joseph Daul and Manfred Weber
Speaking on the MH17 plane incident, they said, "We call once again for an independent international investigation to be conducted without delay and without restrictions," adding, "The way separatist rebels treated the bodies and goods after the crash is a disgrace."
"The current crisis on our European continent shows yet again that the EU needs to stand united and speak with a strong, single voice in the world and in the EU's eastern neighbourhood," they stressed.
"Putting an end to the fighting and bloodshed is the first priority," but to achieve this they highlighted that "Ukraine needs support from the EU, the OSCE and the international community to control its borders.
Daul and Weber were joined by fellow MEPs Elmar Brok, Jacek Saryusz-Wolski, Sandra Kalniete, Cristian Preda and Andrej Plenković for the two-day visit to Kyiv.
During the visit the delegation met with high level Ukraine politicians, including president Petro Poroshenko and then prime minister Arseniy Yatsenyuk, who resigned on Thursday following the breakup of the coalition government.
Yatsenyuk will, however, remain in an interim position until a new government is formed after the next elections, expected to be held in late November.
According to polls, the next government is likely to be pro-western, with pro-Russian parties potentially having no parliamentary presence for the first time since Ukraine's independence.
"Russia must be convinced to contribute to a peaceful solution to the crisis in Ukraine" - Gianni Pitella
Elsewhere, further comment came from parliament's S&D group, with their president Gianni Pittella, saying, "We urge and firmly ask the European commission to propose a collective and strict ban on arms sales to Russia with immediate effect.
"Russia must be convinced to contribute to a peaceful solution to the crisis in Ukraine," insisted the Italian MEP.
"The European Union needs to demonstrate unity and determination to achieve this. The tragic downing of the Malaysian aircraft in eastern Ukraine must be a game-changer, but in a positive sense.
"Sanctions themselves should not, however, be the only goal," he pointed out, "Our common objective is to stop war and the suffering of innocent people in our immediate neighbourhood.
"We will not tolerate any attempt to undermine the Ukrainian territorial integrity and sovereignty," he emphasised.
Meanwhile, German deputy Knut Fleckenstein said that, "In parallel, we need to work on the Ukrainian side.
"Here, there is also a contradiction: part of EU assistance to Ukraine currently serves to repay interests and bills to EU member states and others.
"The S&D group proposes a moratorium on such payments until the Ukrainian economy stabilises. This would be an additional concrete measure to support Ukraine," suggested the S&D MEP.
"Furthermore, we need to encourage the Ukrainians to step up reconciliation efforts. An inclusive national dialogue that takes into account legitimate concerns of local communities and minorities is crucial in this respect," he explained.
"We need to encourage the Ukrainians to step up reconciliation efforts" - Knut Fleckenstein
So far the EU has agreed on further sanctions, adding to the current list of 72 people and two entities that already face visa bans and a freezing of their assets.
The council's committee of permanent representatives has also agreed to extend the 'designation criteria" meaning that sanctions can now be placed on those who are "benefiting from the annexation of Crimea and destabilisation of eastern Ukraine".