Giovanni Carpini in his Ystoria Mongalorum lists as factions under the dominion of the Mongol Empire:
Nations that have been subjugated:
It has been narrowed down to these 5 nations.
The list can be found in the original Latin on page 68 of this edition of the Ystoria Mongolarum, about 1/3 of the way down the page.
On Page 269 (through 295) are C. Raymond Beazley's Notes on Hakluyt's Version of Vincent of Beauvis' Abridgement of Carpini, discussing the text. On Page 278 at the top we have a discussion of India magna (noting that India in this context likely meant everything from Kabul to Saigon, our Indies): as that part of India between the Indus and Ganges rivers, so roughly corresponding to the modern country of India.
Further India would at his time have referred to the territories east of, or beyond, the Ganges, and so to our modern Indo-China, the countries of Burma, Siam, Laos, Malaysia, Cambodia and Vietnam.
Lesser India would have been the territories west of the Indus River, or roughly modern Pakistan and Afghanistan.
Simply perusing the text I recognize the Kytai and Naymani as Mongol tribes (nations) subjugated by Temujin very early on. The Merkiti may also fall in this category.
Note the (often vast) distance between the actual territory being referred to and what a simplistic translation might generate from modern country names. Also, at the time of Carpini's writing there was a mistaken belief in an Asian Abyssinia distinct from the (true) African Abyssinia. This likely is the source of the reference to Aethiopia, the modern country of which name was certainly never under any Mongol suzerainty.
Update - two more: