Aleksandr Borodai, the self-styled prime minister of the self-declared "Donetsk People's Republic," made the announcement today after peace talks with representatives from Moscow, Kyiv, and the Organization for Security and Cooperation in Europe (OSCE).
The talks were chaired by former Ukrainian President Leonid Kuchma.
Borodai said separatists in the self-declared "Luhansk People's Republic" also agreed to a cease-fire until June 27.
He added that separatist officials would join more talks aimed at resolving Ukraine's crisis, which has pitted Ukrainian armed forces against pro-Russian separatist fighters.
The separatists previously rejected a unilateral weeklong truce declared on June 20 by Ukrainian President Petro Poroshenko.
The announcement seemed to affect the situation on the ground, with Ukrainian officials reporting an abrupt halt to insurgent attacks in eastern Ukraine.
Kuchma said that, if both sides observe the cease-fire, then "a normal peace process could start."
In Washington, U.S. President Barack Obama urged Russian President Vladimir Putin to support peace in Ukraine and said Moscow would face further "costs" if it did not take steps to reduce tensions in the country.
The White House said Obama made his comments to Putin via phone today, calling on him to halt the flow of "arms and materiel across the border" and Kremlin support for "militants and separatists."
Obama added that Russia will face additional sanctions if Washington does not see "concrete actions to de-escalate the situation."
Putin, for his part, was said to have emphasized to Obama the importance of direct talks between Ukrainian officials and the pro-Russian separatists in eastern Ukraine.
Earlier in the day, European Union foreign ministers repeated their threat of wider sanctions against Russia if it failed to support Poroshenko's peace plan.
The bloc has so far ordered visa bans and asset freezes for officials but refrained from imposing broader economic sanctions on Russia.
Ahead of an EU foreign ministers meeting in Luxembourg today, British Foreign Secretary William Hague said the EU will be able to agree further measures at a summit of EU leaders on June 27, if necessary.
He said Moscow must be in "no doubt" it faces further sanctions.
Swedish Foreign Minister Carl Bildt accused Russia of "conducting a propaganda war with full speed," adding that Moscow must face further sanctions unless it changes course.
Meanwhile, the European Council said it has finalized technical preparations ahead of the signing of an Association Agreement with Kyiv in Brussels on June 27.
Our correspondent in Brussels is reporting that NATO foreign ministers are planning to set up a trust fund to support Ukraine's defense capacity when they meet in Brussels on June 24-25.
A NATO source tells RFE/RL that the trust fund will focus on boosting Ukrainian defense in areas such as logistics, command and control, and cyberdefense.
No lethal aid to Ukraine has so far been discussed.
At the moment, there is also no decision on a timeline for setting up the fund or how much money will be available.
Officials also say no change is expected in an April decision to suspend all practical NATO-Russia cooperation, amid speculation that a meeting of the NATO-Russia Council would be convened soon to take stock of the situation in Ukraine.
Foreign ministers will also discuss the situation in Afghanistan and review progress ahead of a NATO summit in September in the four countries aspiring for NATO membership -- Bosnia-Herzegovina, Georgia, Montenegro, and Macedonia.
BREAKING: Russian President Vladimir Putin has asked parliament to cancel the authorization to send the Russian Army into Ukraine.
More on Putin's request to the Federation Council from our news desk:
Russian President Vladimir Putin has asked the Federation Council to revoke the authorization it had granted for Russian military forces to intervene in Ukraine.
Interfax quotes a senior Russian senator as saying the Federation Council will withdraw the resolution on June 25.
Russian news agencies quote Putin spokesman Dmitry Peskov as saying the request was made with the aim of "normalizing the atmosphere and resolving the situation in the eastern regions of Ukraine, and also in connection with the start of three-way negotiations."
Putin's announcement comes one day after EU foreign ministers, meeting in Brussels, urged the Kremlin to revoke the March 1 mandate.
EU foreign ministers also repeated their threat of wider sanctions if Russia failed to support a peace plan put forward by Ukrainian President Petro Poroshenko.
Putin has given his cautious support to the plan.
In this piece, Paul Goble picks up on some comments by Moscow commentator Igor Eidman, arguing that "Putin is Carrying Out ‘Biggest Information Special Op’ in Modern Times."
They were “consciously led to a state of mass psychosis. The irrational fear and hatred of the Russian speakers to the new Ukrainian authorities was intentionally provoked with the help of a brainwashing campaign, the dissemination of panic rumors, and the work of Russian media and political technologists.”
No one threatened Donetsk or Luhansk, least of all Kyiv, until the revolt forced the Ukrainian army to intervene. “The population [of the two oblasts] did not need a war” and it has not brought them anything but suffering. “But there are forces interested in provoking the conflict and using the population of these regions for their own selfish interests.”