Cameron promised 3 billion pounds ($3.7 billion) of annual military aid for Ukraine for "as long as it takes" on Thursday, adding that London had no objection to its weapons being used inside Russia.
"Ukraine has that right. Just as Russia is striking inside Ukraine, you can quite understand why Ukraine feels the need to make sure it's defending itself," Cameron told Reuters during a visit to Kyiv.
Russia has in recent weeks pummelled Ukrainian energy infrastructure with missile and drone strikes.
Cameron's comments put Britain in a more hawkish position towards Russia - at least publicly - than the United States, which stipulates that any weapons it supplies to Ukraine should only be used within Ukraine's internationally-recognised borders rather than against targets inside Russia itself.
Ukraine says it uses its own drones and other weapons to launch attacks against targets inside Russia such as oil refineries or railway infrastructure.
Kremlin spokesman Dmitry Peskov described Cameron's comments as dangerous.
"This is a direct escalation of tension around the Ukrainian conflict, which could potentially pose a danger to European security, to the entire European security architecture," he said.
"This is where we see such a dangerous trend of escalating tension in official statements. This is a cause for our concern."
Russian Foreign Ministry spokeswoman Maria Zakharova added:
"This is the first time that a Western politician has so frankly acknowledged what has long been a well-known secret for a majority of the world's countries: That the West is waging a covert war against Russia with the hands of Ukrainians."
Russia would respond if Ukraine launched strikes against Russian territory with British weapons, she added.
"How irresponsible and callous do you have to be not to realise what such statements lead to, especially with regard to countries with nuclear weapons," Zakharova told a briefing.
"We always respond, but how can you not think about the feelings of British subjects and EU citizens."
REUTERS
