The Australian dollar fell to $0.7867 from $0.7877.
The US dollar bought 106.64 Japanese yen, higher than 106.37 Japanese yen of the previous session. The US dollar was down to 0.9439 Swiss franc from 0.9466 Swiss franc, and it was up to 1.2942 Canadian dollars from 1.2828 Canadian dollars.
Tillerson's departure raised market concerns that the Trump administration will institute protectionist policies and be more aggressive in negotiating trade tariffs with other countries.
On the economic front, the Consumer Price Index (CPI) for all urban consumers increased 0.2 per cent in February on a seasonally adjusted basis, in line with market consensus, the US Labor Department reported on Tuesday.
Over the last 12 months, the all items index rose 2.2 per cent before seasonal adjustment.
The dollar index, which measures the greenback against six major peers, fell 0.25 per cent at 89.675 in late trading.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)