WASHINGTON — A treaty committing the United States and Russia to keep their long-range nuclear arsenals at the lowest levels since early in the Cold War goes into full effect on Monday. When it was signed eight years ago, President Barack Obama expressed hope that it would be a small first step toward deeper reductions, and ultimately a world without nuclear weapons.

Now, that optimism has been reversed. A new nuclear policy issued by the Trump administration on Friday, which vows to counter a rush by the Russians to modernize their forces even while staying within the treaty limits, is touching off a new kind of nuclear arms race. This one is based less on numbers of weapons and more on novel tactics and technologies, meant to outwit and outmaneuver the other side.

The Pentagon envisions a new age in which nuclear weapons are back in a big way — its strategy bristles with plans for new low-yield nuclear weapons that advocates say are needed to match Russian advances and critics warn will be too tempting for a president to use. The result is that the nuclear-arms limits that go into effect on Monday now look more like the final stop after three decades of reductions than a way station to further cuts.

Yet when President Trump called on Congress to “modernize and rebuild our nuclear arsenal” in his State of the Union address last week, he did not mention his administration’s rationale: that President Vladimir V. Putin of Russia has accelerated a dangerous game that the United States must match, even if the price tag soars above $1.2 trillion. That is the latest estimate from the Congressional Budget Office, one that many experts think is low by a half-trillion dollars.