Yevgeny Prigozhin will go to Belarus to ease tensions and the fighters of PMC Wagner Group who took part in the so-called "campaign" against Moscow will not be prosecuted, the Kremlin said Saturday evening.

The rest will be able to sign a contract with the Ministry of Defense, the President of the Russian Federation Dmitry Peskov told reporters.

"In the end, we managed to resolve this situation without further losses, without raising the level of tension," Peskov said.

"An agreement was reached that PMC Wagner would return to their camps," he added.

The Wagner Group's chief Yevgeny Prigozhin said he has ordered his mercenaries to halt their march on Moscow and return to their field camps, saying he wants to avoid shedding Russian blood.

Prigozhin made the announcement in an audio message posted on his Telegram channel.

Russian state media has shown Wagner fighters packing up and reportedly leaving Rostov.

Russian President Vladimir Putin has called Belarusian President Alexander Lukashenko and thanked him for his efforts de-escalating the situation.

-ABC News' Patrick Reevell and Tomek Rolski

Gen. Mark Milley, the chairman of the Joint Chiefs of Staff, has canceled his planned trip to Israel and Jordan due to the situation in Russia. The trip was to have begun Saturday.

Milley also spoke with his Ukrainian counterpart, Commander-in-Chief of the Ukrainian Armed Forces Gen. Valerii Zaluzhnyi.

"They discussed the unprovoked and ongoing Russian invasion of Ukraine and exchanged perspectives and assessments. The Chairman reaffirmed unwavering support for Ukraine’s sovereignty and territorial integrity," according to Joint Staff spokesperson Col. Dave Butler.

The Pentagon said Department of Defense Secretary Lloyd Austin is monitoring the ongoing situation in Russia and will continue to be briefed on any significant developments.

-ABC News' Luis Martinez

Andrey Vorobyov, the governor of the Moscow region, has suspended mass events outdoors and at educational institutions until July 1.

Moscow Mayor Sergey Sobyanin urged residents to refrain from traveling around the city. Monday was also declared a non-working day for the city. Sobyanin said that a counter-terrorism regime was declared in Moscow and that the situation was difficult.

-ABC News' Tomek Rolski

Beginning in October, the U.S. will provide F-16 training to a small number of Ukrainian pilots and maintenance teams, Pentagon press secretary Brig. Gen. Pat Ryder said Thursday.

Ryder said "several" pilots and "dozens" of aircraft maintenance personnel will begin training at Morris Air National Guard Base in Tucson, Arizona, after they receive English training in September at Lackland AFB in San Antonio, Texas. The number of pilots and personnel will be determined by Ukraine.

"Although some Ukrainian pilots have English language skills we are anticipating that all the pilots coming to the United States will require some level of additional English language instruction, given the complexities and the specialized English that's required to fly these aircraft," said Ryder.

Sabrina Singh, the Pentagon's deputy press secretary, told reporters earlier this week that the U.S. was open to the idea of training on F-16's if European countries reached capacity though she couldn't define what numbers would constitute capacity. Ryder on Thursday also wouldn't provide a number and said the U.S. wasn't going to wait for the Netherlands and Denmark to reach capacity.

"We know that as the Danes and the Dutch prepare to train those pilots that at a certain point in time in the future, capacity will be reached. So preemptively acknowledging that and leaning forward in order to to assist with this effort is the impetus for why we're doing this now," said Ryder.

Ryder wouldn't get into when F-16 deliveries to Ukraine might begin. Denmark's Prime Minister said over the weekend that the first Danish F-16's could arrive by New Year's.

-ABC News' Luis Martinez