Russian spies have flooded the US to infiltrate government, businesses and other institutions as President Vladimir Putin has dramatically expanded intelligence operations on US soil, a new report said Monday.

“There are more Russian operatives, declared and undeclared, in the United States now than at any other time in the past fifteen years,” a senior US official told The New Yorker.

“They’re here in large numbers, actively trying to penetrate a whole host of sectors—government, industry, and academia.”

And the FBI does not have sufficient resources in the field to track down and identify the swarms of spooks, according to the stunning report.

The Bureau has “a math problem. It takes a lot of folks to run surveillance on one individual and make sure you never lose contact,” the official said.

The magazine said that two Russian operatives met with someone they believed was a White House mole to try to get inside information about how the Obama administration would respond to Russia’s interference in the US presidential election in favor of Donald Trump.

But the mole turned out to be an American counterintelligence asset, and the Russians left the sitdown empty handed.

Then, on Dec. 29, the Obama administration announced that 35 Russian diplomats linked to the meddling would be booted from the US.

But that effort affected just the tip of the Russian spy network’s iceberg.

“The number of folks who were sent home is a fraction of those who could have been sent home,” the officials said.

The White House expected Russia to retaliate, but Putin soon announced there would be no tit for tat.

And it was later revealed that then-presidential adviser Mike Flynn had hinted to the Russians that President Trump could ease the sanctions.

The imbalance between the Russian and US spy operations is compounded by Russia’s tougher stance on ferreting out CIA operatives on its soil.

“The Russians make it extremely difficult for American intelligence officers to operate in Russia, in a way that would be nearly impossible for the FBI to do the same here,” because constraints imposed by the US legal system, Steve Hall, a former CIA station chief in Moscow, told the magazine.

The Russian operation, he added, had not shrunk even though the Cold War had ended.

“It’s consistent to say that the resources and times and effort that it takes to run successful operations inside of Russia has not changed since Cold War times,” Hall said.

Last week, Putin retaliated against tough new sanctions imposed by Congress — which Trump reluctantly signed off on — by ordering that 755 embassy and consular staffers be expelled, further weakening the US presence in Moscow.

Secretary of State Rex Tillerson said Sunday that the Trump administration would decide what retaliatory action to take against the Kremlin by the end of the month.

Tillerson said he shared that deadline with Russian Foreign Minister Sergey Lavrov when they met that day in Manila.

The president has repeatedly called special counsel Robert Mueller’s probe of Russia and its possible ties to the Trump campaign a “hoax,” “fake news” and a “witch hunt” despite confirmed contacts between his top advisers and Russian officials and others connected to the Kremlin.