The summit's final statement said the participants "call on all actors to refrain from any activities exacerbating the conflict or inconsistent with the (U.N.) arms embargo or the ceasefire, including the financing of military capabilities or the recruitment of mercenaries".
The foreign minister said the Berlin Conference on Sunday was a "good first step" but expressed Greece's displeasure at the absence of any explicit reference in its final conclusions to the European Union position on the memoranda signed by Turkey and the Tripoli government in Libya, to state that these were illegal and invalid.
Sarraj also said his government would respect the summit's decision to turn a tentative ceasefire into a permanent truce in Tripoli and open intra-Libyan talks to end conflict as part of a UN-led plan.
He said Turkey would do whatever was necessary if Haftar and his so-called Libyan National Army (LNA) did not abide by the agreement.
Libya has been in turmoil since its former leader Muammar Gaddafi was killed in 2011, with the support of NATO-backed forces. For more than five years it has had two rival governments, in the east and the west, with streets controlled by armed groups. But the fight for the capital, Tripoli, has generally been stalled since April with hundreds of thousands of civilians caught in the middle.
Since the ouster of late ruler Muammar Gaddafi in 2011, two seats of power have emerged in Libya: warlord Khalifa Haftar in eastern Libya, supported mainly by Egypt and the UAE; and the Government of National Accord (GNA) in Tripoli, which enjoys the United Nations and worldwide recognition.
Unofficial diplomatic reports from Russian Federation said Haftar had refused to sign the Berlin agreement, and for parts of the summit had turned off his phone, before leaving early.
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The agreements at the Berlin conference are largely contingent on the two sides wanting to implement a ceasefire rather than seek military victory.
United Nations experts and diplomats say Russian military contractors in recent months have deployed alongside Haftar's LNA, which has also received air support from the U.A.E. and backing from Jordan and Egypt.
"We know that we have not solved all of Libya's problems today but we were aiming for fresh momentum", she said at the end of the gathering.
She added the conference hadn't discussed specific sanctions for violating the arms embargo.
UN Secretary-General Antonio Guterres confirmed that these representatives were named in Berlin on Sunday. "I had the opportunity to speak on behalf of the Greek government and to describe the Berlin conclusions, initially, as a good first step", Dendias said.
Mr Guterres said that the committee would be convened "in Geneva in the coming days".
Still, the president made it clear that he does not see Turkey's role as that of a mediator in Libya.
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Among those attending were Russian President Vladimir Putin, Turkish President Recep Tayyip Erdogan, French President Emmanuel Macron, Italian Prime Minister Giuseppe Conte, British Prime Minister Boris Johnson and US Secretary of State Mike Pompeo.
Erdogan met Putin before the summit began, with Putin saying "we will sincerely strive for the conflict to be resolved".
In a sign the situation was deteriorating, the Libyan National Oil Corporation (NOC) reported that forces directly under the instruction of Haftar had blocked oil exports from Brega, Ras Lanuf, Hariga, Zueitina, and Sidra ports.
Erdogan said Turkey's presence in Libya raises hopes for peace.
On Sunday, as worldwide leaders were gathering in the German capital, state oil firm NOC said the major southwestern fields of El Sharara and El Feel were closing after forces loyal to Mr Haftar shut a pipeline.
He also said: "Joint efforts on Libya provided relative calm in the field but our initiatives will reap fruits with the Berlin conference".
Libya's economy is depended on oil and Guterres says he is "very anxious".
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Underlining the stakes involved, German Foreign Minister Heiko Maas said "we have to make sure Libya doesn't become a second Syria".