The US said the deal would not affect the military balance in the region
The US government has notified Congress of plans to supply Taiwan with arms worth more than $6bn (£3.4bn).
The sales include advanced interceptor missiles, Apache helicopters and submarine-launched missiles.
Correspondents say the decision is likely to anger China, which regards Taiwan as its territory and opposes US military support of the island.
The move could also complicate efforts to get North Korea, an ally of Beijing, to end its nuclear programme.
The US Defence Security Co-operation Agency (DSCA) said the sales would "help improve the security of the recipient and assist in maintaining political stability, military balance and economic progress in the region".
DSCA said the deal would not alter the military balance in the region but was "a demonstration of the commitment of this administration to provide Taiwan the defensive arms its needs to be strong".Congress members have 30 days to submit comments or objections about the proposed sale.
US Air Force Secretary Michael Wynne was "very concerned"
The shipment, which should have been helicopter batteries, was made in 2006 but only discovered last week.
The Pentagon says no nuclear materials were shipped and the parts have been returned to the US.
The issue of US arms sales to Taiwan is sensitive as China regards the island as a renegade province.
The BBC's Jane O'Brien in Washington says senior officials have described the incident as "disconcerting" and "intolerable".
Taiwan had pointed out the error, but owing to a two-year miscommunication the US administration remained unaware of it until last week.
The shipment had been sent from a US airbase in Wyoming.
Our correspondent says the components are not in themselves nuclear material but do form part of a long-range missile system that could deliver a nuclear weapon.
Air Force Secretary Michael Wynne said: "It is a component for the fuse in the nose cone for a nuclear system. We are very concerned about it."
President George W Bush and the Chinese government were informed about the error.
Beijing vehemently opposes US arms sales to Taiwan and has threatened to attack the island if it declares independence.
The mistaken shipment is the second blunder in recent months.Last August a B-52 bomber flew across several US states mistakenly armed with nuclear-tipped cruise missiles.