The announcement, made by General Charles F. Wald, Deputy Commander of US European Command after talks with Azeri President Ilham Aliyev, marks a dramatic ramping up of the US military presence in the strategic region.
General Wald said the Azeri government had agreed to make its facilities available so that US forces could deploy temporarily to the country, though he ruled out a permanent presence in Azerbaijan.
He added that his command was seeking permission from US Defence Secretary Donald Rumsfeld to send instructors to train the Azeri military, in a programme similar to one being run in neighbouring Georgia.
"We would like the opportunity to come here temporarily for a short period of time with various forces to train and be better able to work together and establish inter-operability and to show our commitment to the region," the general told reporters at a press conference.
He added: "We hope and we know that the Azerbaijan authorities agree with us on this."
The Pentagon wants a presence in the region to counteract what it sees as a threat from terrorism and the proliferation of weapons of mass destruction.
It is also keen to protect exports of oil from the Caspian Sea to Western markets. A US-backed pipeline crossing Azerbaijan, Georgia and Turkey is due to come on stream at the beginning of 2005.
However, an increased US military presence is likely to be received coolly by Azerbaijan's neighbours, Russia to the north and Iran to the south.
Moscow in particular views the region as part of its sphere of influence and reacted angrily when US military instructors were deployed to Georgia.
But Wald sounded a reassuring note, saying that "we do plan to work with the Russians as closely as possible to make sure that the way ahead is a shared strategy."
The Pentagon floated the idea of a US military presence in Azerbaijan last year, but the details are now being hammered out by both sides.
Azerbaijan is a predominantly Muslim state of eight million people on the western shore of the Caspian Sea. Its pro-Western government has backed the US-led war on terrorism and it has sent contingents of troops to both Iraq and Afghanistan.
Asked what form the deployment of US forces in Azerbaijan could take, General Wald said: it could be "from a naval standpoint, it could be special forces, it could be ground operations."
The general, on his second visit to Azerbaijan in three months, ruled out the establishment of US bases in the country.
But he added: "It is in our interests if the Azerbaijan government, say, improves the facilities at one of the air bases and if we came here and temporarily used it it would be able to accommodate our aircraft."
He said the planned training of Azeri troops would be along the lines of the Georgia Train and Equip Programme, under which some 150 US Green Beret special forces instructors have been stationed in Georgia training about 2,000 local troops.
Wald said that his superior, Supreme Allied Commander, Europe, General James L. Jones, will be advising the Pentagon to establish a similar programme in Azerbaijan.
"We have been in Georgia training the military for the last year and a half," the general said. "We see the benefits of that, having experience of working with the Azerbaijan forces, from the point of view of interoperability with US forces."
"It has not been approved but we think it would be a good idea and the civilian administration in Washington agrees with that."