GENEVA, April 17 -- Four-way talks in Geneva over the Ukraine crisis concluded on Thursday with a document on de-escalation of tension in Ukraine, Russian Foreign Minister Sergei Lavrov said after the talks.

The high-level meeting brought together European Union High Representative for Foreign Affairs and Security Policy Catherine Ashton, Russian Foreign Minister Sergei Lavrov and U.S. Secretary of State John Kerry and Ukrainian Acting Foreign Minister Andriy Deshchytsya for the first time since the crisis began, in an effort to initiate a dialogue to seek ways to handle the intensified development in Ukraine.

The diplomatic endeavor ran hours beyond original schedule, signaling the difficulty of achieving common ground among the four parties for a potential solution to the current crisis.

According to the statement issued after the meeting that detailed the agreement reached by the four sides, initial concrete steps to de-escalate tensions and restore security for all citizens include that all sides must refrain from any violence, intimidation or provocative actions.

Moreover, all "illegal armed groups" must be disarmed, and all "illegally seized buildings" must be returned to legitimate owners, and all "illegally occupied" streets, squares and other public places in Ukrainian cities and towns must be vacated, the statement said.

Amnesty will be granted to protestors and to those who have left buildings and other public places and surrendered weapons, with the exception of those found guilty of capital crimes, according to the statement.

It was also agreed that the Organization for Security and Co-operation in Europe (OSCE) should play a leading role in assisting Ukrainian authorities and local communications in immediate implementation of these de-escalation measures.

Besides, the participants highlighted that the announced constitutional process in Ukraine will be "inclusive, transparent and accountable," which would include the immediate establishment of a broad national dialogue outreaching to all regions and political constituencies in Ukraine and allow for the consideration of public comments and proposed amendments.

All parties also underlined the importance of economic and financial stability in Ukraine.

"We wanted to find concrete steps, not just words, but concrete steps that could be acted on immediately in order to defuse the situation," Kerry told a press conference upon the talks conclusion.

He highlighted the importance of the OSCE's role in de-escalating the tension.

Kerry stressed the urgency of taking actions under the agreement. "What is vital is that the OSCE needs to get to work immediately, to de-escalate the situation" in eastern Ukraine, he said.

"If this starts and starts effectively, and we can begin to see some progress, we intend to continue to have our meetings... continue to talk to follow up on this," Kerry added.

As for the specific time frame for these steps to be implemented, Kerry said that "we expect in the next few days, over the course of this weekend and the earliest part of next week, some of these steps need to begin to be seen and be evident."

Moreover, Kerry said there was no discussion at this point in time of removal of any of the existing sanctions against Russia, and the West and Russia remain differed significantly on the Crimea issue.

Ashton said the talks have been "frank" and "constructive" and sought to find "the concrete steps, real, practical things that can de-escalate the tensions in Ukraine."

"I think it was extremely important to bring us all together here to have that process of dialogue begin," the EU foreign policy chief said. "We agreed a number of concrete steps that we can see implemented immediately."

Ashton expected a "free and fair" presidential election scheduled next month in Ukraine, and welcomed the "Ukrainian commitment to conduct an inclusive and transparent constitutional process."

She reiterated the EU's determination to continue to support efforts to stabilize the situation in Ukraine economically, financially and politically.

Deshchytsya told reporters after U.S.-EU joint press conference that the next days would be crucial and sincere efforts from all participants are required so as to put into practice the agreement concluded on Thursday.

"It is important that these measures are to start being implemented in the coming days," said Deshchytsya.

"We disagree with Russia on many things, but what we agreed today is to put an effort, joint efforts, to launch the process of de-escalation in eastern Ukraine," he said.

Moreover, Deshchytsya said Kiev was ready to negotiate with Moscow about the gas price, which would be based on the market ground rather than political pressure.

A new wave of tension erupted in the country's east over the weekend, as pro-Moscow activists seized several administrative buildings in nearly 10 eastern cities, demanding a referendum on autonomy and closer ties with Russia.

The developments came after Russian President Vladimir Putin and Crimean leaders signed a treaty on March 18 to make Crimea part of Russian territory, as almost 97 percent of voters on the peninsula backed secession from Ukraine in a referendum.

Earlier this week, Kiev began military operations against pro-Russia militants occupying government buildings in the eastern part of the country.