O'Connor said he hopes to "complete the final steps of our FTA negotiations".
The guts of the FTA were announced last year.
O'Connor said in Europe he would "meet with European Union counterparts to advance our FTA talks in Brussels".
"That will be followed by a visit to the World Trade Organisation in Geneva".
The trade agreement with Europe is advanced, but talks had slowed over a gap in ambition between Europe and New Zealand on goods market access.
In the Middle East, O'Connor will attend Expo 2020 in Dubai.
He said the trip "provides the opportunity to also engage with the Gulf Cooperation Council when in the Middle East".
"Our trade agenda has very good momentum. We are now reconnecting with a post-Covid world and unlocking opportunities that will drive our economic recovery from the pandemic," O'Connor said.