The US president will allow Ukraine to use US-made Atacms rockets with a range of 190 miles - the first time the outgoing president has given Kyiv permission to use any long-range weapons inside Russia.
Meanwhile, Kyiv announced that nationwide energy rationing would begin today after Moscow's largest-scale drone and missile attack in months on Ukraine's energy grid at the weekend.
The decision on the use of US weapons - first reported by the Reuters and Associated Press news agencies and the New York Times citing multiple sources - has been long requested by Ukraine.
Russia has said it will regard the move as a major escalation.
Officials suggested the decision was intended to send a message to North Korea, which has deployed troops in Kursk, although Biden may also authorize the use of the Atacms elsewhere. The first strikes could come within days.
The order may not apply to UK-supplied Storm Shadow missiles, whose use at targets on Russian territory the US has previously blocked.
Ukraine has said it wants to deploy Storm Shadows against airbases used to launch attacks on Ukraine.
The White House and Downing Street declined to comment.
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