The attacks, using lorries packed with explosives, claimed 38 victims, says the government-owned Rossiyskaya Gazeta.
"All five terrorist acts bear the same hallmark and are most likely to have been planned in advance," it says.
The lorry used in Urus-Martan was driven by one-legged Movladi, a prominent rebel, claims the paper, adding that suicide bombers are the terrorists' last remaining trump card.
The terrorist acts in Chechnya are a revenge for the rout of 200 Arab mercenaries last week, reports the conservative Trud.
It quotes a top military official as saying that the federal forces are "in full control of the situation".
The paper also quotes rebel Chechen president Aslan Maskhadov's statements made from his mountain hideout.
"The tactic of mine warfare, chosen by the fighters, gives Russian troops no chance to establish control in Chechnya," Mr Maskhadov is quoted as saying.
This proves that he had personally ordered the recent wave of terror, says the paper.
Homes raided
Still on the Chechen theme, Rossiyskaya Gazeta publishes a long article which describes, in graphic, and sometimes gory detail, how Chechen 'bandits' broke into a detached home owned by a Russian family in Grozny.
Two held the elderly woman who owned the house whilst a third savagely beat her.
Her screams eventually woke her son who rushed to her aid. Armed only with a pick-axe, he attacked her mother's assailant, splitting his skull open.
The others pursued him, but he managed to escape.
Sheltered for a while by neighbours, he was eventually persuaded to leave Chechnya, where blood feuds are taken very seriously.
His mother was never heard from again and the paper says that a Chechen family is now living in the house.
The paper publishes the full address of the house and says that this type of crime is not an isolated incident - the elderly have been an easy prey to bandits eager to take over their homes "legally".
Once kidnapped and tortured, the old people would eventually sign on the dotted line and subsequently disappear.
The new "owners" were thus able to show perfectly properly completed sale and purchase documents in amongst their property deeds.
The paper wonders how those who try to build their own happiness on the grief of others live now and what they teach their own children.
It warns them that their deeds have not escaped the eye of their god.
Similarities
Meanwhile, the liberal Sevodnya draws attention to increasing parallels between Chechnya and the Afghan campaign of the 1980s, with Russian federal forces coming under attack from the rear in the so-called liberated territories.
The recent terrorist attacks make it clear that no matter whom Moscow appoints to the positions of power in Chechnya, if the appointees fail to control the rebels, Russia will never be able to establish control over the breakaway republic, it concludes.
BBC Monitoring based in Caversham in southern England, selects and translates information from radio, television, press, news agencies and the Internet from 150 countries in more than 70 languages.