Pro-Kremlin youths say they will end a blockade of the Estonian embassy in Moscow, staged in protest at the moving of a Soviet war memorial in Tallinn.
Pro-Kremlin youths want an apology from Estonia
A spokeswoman for the Nashi group said they would still seek an apology from Estonia for the memorial's removal.
Nato, the EU and US have urged Russia to stop threats against embassy staff, but Moscow dismissed criticism, saying police ensured protests were peaceful.
Estonia closed its consulate after attacks on its diplomats.
Ambassador Marina Kaljurand has gone on leave, originally planned for the end of April, Estonian officials said.
Meanwhile Russia suspended oil supplies by rail through Estonia, but said the stoppage was not for political reasons.
Correspondents say the move could revive Western concerns that Moscow is using its oil and gas reserves as a political weapon against its former Soviet neighbours.
The Russian transport firm Severstaltrans says it is suspending construction of an $80m (£40m) car plant in Estonia.
Estonians of Russian origin rioted last week after the controversial statue of a Soviet soldier was moved away from the centre of Tallinn.
One person died and 153 were injured in the unrest.
Estonians say the soldier symbolised Soviet occupation. Russians describe it as a tribute to those who fought the Nazis.
Russian Foreign Minister Sergei Lavrov said Estonia's decision to move the statue had "led to seriously negative consequences for Russian-Estonian relations".
In a phone call to his Estonian counterpart Urmas Paet, he said the Moscow protest would be kept within the law.
Mr Lavrov called on Estonia to investigate the death which occurred during the Tallinn riots.
A Nato statement urged the two sides to resolve the row diplomatically.
1918: Estonia gained independence from Russia
1940: Forcibly incorporated into Soviet Union
1941-1944: Occupied by Nazi Germany
1944: Soviets return as Nazis retreat
1991: Gains independence as Soviet Union collapses
1994: Last Russian forces leave Estonia
Now: Ethnic Russians make up quarter of Estonia's 1.3m people
"Nato is deeply concerned by threats to the physical safety of Estonian diplomatic staff, including the ambassador, in Moscow, as well as intimidation at the Estonian embassy," the statement said.
On Wednesday, Estonia's foreign ministry said there was an attempt to physically assault Ms Kaljurand at a news conference, as members of "Nashi" tried to disrupt it.
It said the incident amounted to a violation of diplomatic conventions.
Reports said Russian police also scuffled with activists outside the Estonian embassy, arresting one person as protesters attempted to prevent diplomats entering or leaving the building.
Following the disturbances, the European Union said it would send a delegation to raise concerns with Russia over the increasing violence.
US State Department spokesman Tom Casey called on the Moscow authorities to do everything they could to reduce tensions.
More than a quarter of Estonia's 1.3 million people are ethnically Russian, and speak Russian. However, half of them do not have Estonian citizenship.
During the years of Soviet occupation after the war tens of thousands of Estonians were killed. They say their country was effectively colonised, with many Russians being brought in as workers and military personnel.