The greenback traded in a limited range on Tuesday, as investors maintained their caution ahead of the release of important U.S. inflation data later during the day.

The market's focus now shifts to the U.S. Labor Department's CPI report, which is scheduled to be released later on Tuesday and is anticipated to reveal that inflation moderated slightly in May. If this is the case, it may allow the Fed to stop its hawkish rate hikes.

According to the CME FedWatch tool, markets are presently pricing in a probability of about 84% that the Fed will decide to keep interest rates on hold this week.

The US dollar index fell 0.17% to 103.40, staying close to Monday's low of 103.24, its lowest level since May 23.

EUR/USD railed at $1.0792, the highest level touch since May, as traders were paying attention to the European Central Bank's policy meeting decision on interest rates that would be announced on Thursday.

GBP/USD added 0.16% to $1.25315, Following reaching a one-month high of $1.2600 on Monday.

USD/JPY dipped 0.06% to 139.52.