But if their plan was to bring more chaos, they may have succeeded. The suspension of many International Committee of the Red Cross (ICRC) operations, the largest in the former war zone, is a heavy blow for Chechnya, which lies in ruins after 21 months of war.
Chechnya's neighbours have also been hit. The UN High Commissioner for Refugees (UNHCR), which has no staff in Chechnya itself, last night said it had halted work in the neighbouring republics of Dagestan, Ingushetia and North Ossetia for security reasons. High Commissioner Sadako Ogata expressed deep concern at the lack of security for aid workers at a Geneva meeting with Russia's Deputy Foreign Minister, Nikolai Afanasievsky, a spokeswoman said.
With precious little money coming from Moscow, the ICRC was meeting a desperate need. It was reopening schools, feeding thousands of people, providing medical care to the hoards of rural Chechens whose homes and lives were wrecked as the Russian army mounted one attack after another on civilian settlements. With peace at last - albeit an uneasy one - the agency was at last able to get on with reconstructing the sewage system under the wrecked city of Grozny, the republic's capital, which has been flooded and is in danger of leaking into the fresh water supply.
The agency was not always welcome - some zealous local Chechen Muslims had complained about its use of the cross as a symbol, but few could deny that it was providing a crucial service. Not any more, at least for the time being.
There was a belief yesterday, among the Chechen leadership and among many in Moscow that the murders, which appeared to have been "professionally" carried out, were politically motivated.
The presumed aim was to disrupt the elections in Chechnya, scheduled for 27 January which form a key component of the peace deal with Moscow. The Chechen leadership and, at least ostensibly, the Kremlin were keen for the elections to be seen worldwide to be legitimate. International observers were to be invited.
Now foreign participation seems far less certain. So the opponents of the Chechen peace deal may well be able to claim that the results of the elections, which will create a separatist president, are questionable. They may now have to be delayed for this reason.
There are many such opponents.These include hard-line nationalist elements in Russia, including senior members of the security forces who were furious at President Boris Yeltsin's recent decision to withdraw all Russian troops from Chechnya.They regard the peace accord as an admission of defeat and a capitulation to terrorists.
The Chechens also have extreme voices who have made clear their loathing of the peace deal. For the last four days, Salman Raduyev, a radical Chechen commander, has been holding 21 troops from the Russian Ministry of Interior hostage, apparently in protest over the accord. That accord postpones a final settlement of Chechnya's status for five years. He has reportedly said the war should go on until Chechnya wins outright independence.
Yesterday Ivan Rybkin, the head of Russia's Security Council who recently replaced the sacked General Alexander Lebed, arrived in Grozny, where he condemned the killings (as did Russia's Prime Minister, Viktor Chernomyrdin) and told reporters Raduyev's hostage-taking was a "pitiful failure".
As it dispatched aid workers to safety in the nearby Russian ethnic republic of Kabardino-Balkaria, the Red Cross made clear it was unwilling to resume full operations without a guarantee that its foreign workers would be safe. The murders, said a spokesman in Moscow, were "an assassination".
Such guarantees will be hard for the separatists who now run Chechnya to give, unless the killers are caught. Yet without Red Cross help, Chechens will have to struggle on, living in the wreckage of a war without adequate health care, water, or housing. The sorry history of a long-suffering people will only grow grimmer.