Acting Defence Secretary Patrick Shanahan said the deployment was in response to what he described as “hostile behaviour” by Iranian forces.
Tensions were further fuelled on Monday when Iran said its stockpile of low-enriched uranium would next week exceed levels set under the 2015 nuclear agreement.
Iran’s President Hassan Rouhani said his country did not seek to wage war with any nation and had remained “loyal” to its international obligations.
What do we know about the extra troops?
The US troop deployment to the Middle East was announced by Mr Shanahan late on Monday.
In his statement, he said the “United States does not seek conflict with Iran” but the action was taken to “ensure the safety and welfare of our military personnel working throughout the region to protect our national interests”.
He said the military would continue to monitor the situation and make adjustments to troop levels accordingly.
Monday’s troop increase announcement comes on top of 1,500 extra announced by President Donald Trump last month.
The 1,000 additional troops being despatched to the Middle East is presented as a prudent defensive measure by the Pentagon; the recent attacks on the two oil tankers being taken as a clear sign of Iran’s hostile intent.
They join some 1,500 additional troops sent last month. Taken together, these deployments inevitably raise tensions but they are clearly not in any sense an assault force.
If direct conflict does break out between Washington and Tehran, it will most likely be a sporadic air and maritime battle, not a land campaign.
The US defence secretary is again insisting that Washington does not want conflict with Tehran, but tensions remain high and any miscalculation could lead to a serious escalation.
What do the latest images show?
Shortly before the announcement, the Pentagon released new images including some purporting to show the remnants of an unexploded mine on a Japanese-owned oil tanker.
The photos appear to show it being removed by members of the Iranian Revolutionary Guard Corps. The Pentagon has already released grainy video said to show the same episode.
Also seen in the latest images is apparent damage – a hole – above the waterline on the hull of the Kokuka Courageous vessel.
Another image claims to show the Iranian Revolutionary Guard Corps vessel shortly after it was involved in removing the limpet mine.
A Norwegian-owned tanker, the Front Altair, also reported being hit by the blasts on Thursday.
How do other sides see the situation?
Russia – another party to the nuclear accord – also called for restraint, calling US actions “truly provocative”.
But EU foreign ministers meeting on Monday warned against jumping to conclusions and backed UN calls for an independent investigation.
Why are there new tensions?
In 2015, Iran agreed to a landmark deal with world powers to curb its nuclear development.
It agreed to limit the enrichment of uranium, which is used to make reactor fuel but also nuclear weapons, and other measures in return for relief from sanctions.
Mr Trump abandoned the nuclear accord last year and started to re-impose sanctions.
On Monday, a spokesman for Iran’s Atomic Energy Organisation said it was on course to exceed agreed limits on its low-enriched uranium stockpiles by 27 June.