Otherwise, the United States would feel "completely protected" and able to "do whatever they want".
The US this year dropped controversial plans for missile defence bases in the Czech Republic and Poland, but said it would develop other defensive systems.
Mr Putin said such plans were hindering nuclear arms reduction talks.
Russia and the US are yet to find a successor to the Cold War-era Start I treaty, which expired on 5 December.
The 1991 treaty led to deep cuts in nuclear arsenals on both sides.
Both sides have agreed to continue observing Start I until they reach a new agreement.
Under a joint understanding signed in July, deployed nuclear warheads should be cut to below 1,700 on each side within seven years of a new treaty - a huge cut on Soviet-era levels.
Nonetheless, between them the two countries will retain enough firepower to destroy the world several times over.
'Correct and brave'
"To preserve the balance, we must develop offensive weapons systems, not missile defence systems as the US is doing," Mr Putin said during a visit to Russia's Far East.
"The problems of missile defence and offensive arms are very closely linked.
"By building such an umbrella over themselves our [US] partners could feel themselves fully secure and will do whatever they want, which upsets the balance," the Russian premier added.
Mr Putin did not say what kind of offensive weapons Russia was seeking to develop.
Earlier this month, President Dmitry Medvedev said Russia would continue to develop new nuclear missiles and launchers despite the disarmament talks, describing this as "routine practice".
In September, Mr Putin described as "correct and brave" a decision by US President Barack Obama to shelve controversial missile defence bases in Poland and the Czech Republic.
Mr Obama did, however, say Washington would develop new ballistic missile defences elsewhere, including a sea-based system.
He said the US still needed a programme to defend the US against missiles from "rogue states" like Iran.
Moscow had long objected to plans by the administration of former-President George W Bush to base a missile interceptor system close to its borders, calling it a threat to its security.
