The death of Wagner leader Yevgeny Prigozhin may offer new opportunities to tackle the mercenary group, Britain's Foreign Office has said.
It follows a move by the government to re-examine the "extent and scale" of its intelligence work on the proscribed organisation, following a critical report by MPs.
The private military firm, whose former leader was killed in a plane crash in the summer, was officially designated a terrorist group in September after the Commons Foreign Affairs Committee warned that ministers were not doing enough to counter the threat Wagner posed.
The report by MPs came after Mr Prigozhin and his troops staged a short-lived coup against the authorities in Moscow, pitting the group against the rule of Russia President Vladimir Putin.
Deemed a transnational criminal organisation by the US, the private army is largely made up of convicts, neo-Nazis and white supremacists.
Wagner played a key role in Russia’s war in Ukraine and Mr Prigozhin took credit for several battlefield victories, including the capture of the strategic eastern Ukrainian city of Bakhmut.
But he was regularly at loggerheads with authorities in Moscow, who he accused of not arming the mercenaries properly. He also accused Russia of lying to the public about the justification for invading Ukraine.
UK ministers have backed or partially agreed with the vast majority of MPs' recommendations in the committee’s report, which was published on Monday.
The Foreign Office confirmed a cross-government task force to focus on the group had been set up, telling MPs: "We agree with the committee that intelligence-gathering on Wagner's activities is a priority and have re-examined the extent and scale of our effort.
"We believe that we have sufficient resources in place to track Wagner. Wagner is multi-layered, complex and dynamic.
"We regularly assess the group and its impact. We are also in close contact with international partners, academics and think tanks, and access a wide range of open and closed source reporting in order to inform our approach to countering the organisation.
"Given the fast-moving nature of events surrounding Wagner, that body of work is being continually refreshed, most recently in light of the June mutiny and the demise of Wagner's senior leaders."
The Foreign Office also said it had "dedicated new resources to containing and countering Wagner" and other Russian private military companies, while also working with allies to "maximise our collective impact".
The Foreign Affairs Committee had urged the government to use the uncertainty to "disrupt" the Wagner Group.
In response, the Foreign Office said the death of the Wagner kingpin had the possibility to create "new opportunities" to tackle the group.
Officials said the government was using its "overseas network and strategic communications channels to highlight Wagner's human rights abuses and its destabilising role. We have also stepped up our assessment and policy co-ordination with western and regional partners".
"We plan to continue these activities following Prigozhin's death – an event that may create new opportunities."
The government has also linked the mercenaries to "serious acts of violence and damage to property while working in a variety of African countries, demonstrating Wagner's broader involvement in terrorism".
Committee chairwoman Alicia Kearns praised the "positive response" from the government.
"Efforts to counter the Wagner network have stepped up in recent months and we are pleased that the Foreign Affairs Committee has been able to contribute to this work," she said.
"Private military companies [PMCs] are a clear threat to global security and the rules-based international order. The proliferation of the Wagner network across four continents should be a wake-up call for the UK government: for too long we have underestimated and neglected this group, and the issue of PMCs more broadly."
She added: "The crimes committed by the Wagner network fall heaviest on innocent people in territories where Wagner maintains control for corrupt elites. Steps to counter this ruthless group are welcome – but there is still more to be done."