In an executive order released by the White House on Friday, Trump said the waiver was in the national interests of the United States.
The law is meant to increase pressure on Russia for its invasion of Ukraine that began in 2022.
Trump, however, has been warming towards Russia and publicly criticising Ukrainian President Volodymyr Zelenskiy, including suggesting Kyiv needs a new leader.
Weeks before the US midterm elections in which Trump's Republicans are battling to maintain their narrow grip on both chambers of Congress, the new measures could have risked raising oil prices even further while Americans already face increased costs largely attributed to the US-Israeli war on Iran, analysts have said.
The legislation's primary backer in Congress was the late Republican senator Lindsey Graham.
It would have imposed tariffs of up to 100 per cent within 30 days on all goods brought into the US from the five largest importers of Russian crude oil or gas, as well as any country that knowingly bought oil or gas 30 days after the law was enacted or was among the top five countries helping Russia evade sanctions.
The order said the waiver would remain in effect until Trump or his top officials determined that "further action is appropriate".
Trump signed the Lindsey O Graham Sanctioning Russia and Iran Act of 2026 in mid-September.
"I have submitted to the Congress a certification that the issuance of such a waiver at this time is in the national interests of the United States," Trump said in the order.
Countries such as China and India, which are among the biggest buyers of Russian oil, have raised concerns about the Russia sanctions bill.
Beijing has said it "consistently opposed long-arm jurisdiction that lacks a basis in international law" while India warned Washington that new tariffs could impact bilateral ties.
The law allows the president to waive sanctions simply by informing Congress that he has determined that they are not in the national interest.
US representative Don Beyer, a Democrat, blasted Trump for the waiver, saying he was giving in to Russian President Vladimir Putin.
"Trump's latest surrender to Putin again betrays our Ukrainian partners and defies clear congressional intent of legislation designed to punish Russia for its illegal war of aggression," Beyer said in a statement.
Trump had also faced criticism from several US senators, including some Republicans, over a recent diesel deal with Russia in which Trump agreed to lift sanctions on Russian exports and Russia agreed to supply diesel to global markets in an effort to lower fuel prices.
The lawmakers who criticised the deal said it would help fund Russia's war efforts.
