Fiji beat Uruguay 47-15 in their final Pool A match on Tuesday to end the tournament on a high after defeats against England, Australia and Wales.
"I know there's a lot of speculation in the media with Japan looking for a new coach when Eddie (Jones) leaves at the end of this tournament,” McKee told reporters. “But I am committed to Fiji and when I return I want to discuss with the board the possibility of extending my contract (until 2019).
"I’m contracted until 2017 at the moment and I want to stay there until then, but I feel (that) if I’ve gone all that way with them I should really stay until after RWC 2019 at least."
Fiji caused problems for England, Australia and Wales in the tournament's toughest group.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
“For Fiji it's been a very good tournament, frustrating in a way that we weren’t more successful in terms of results, but we knew we had some massive challenges coming here and being in Pool A,” McKee said.
“We played well against the Tier 1 nations and we had high hopes and perhaps if we caused an upset or got a result against England, Wales or Australia we could have got through. Sadly it wasn’t to be.”
Fiji have made huge strides since McKee took charge 18 months ago, particularly in the scrum.
"There was a lot of talk before the tournament on our set plays and our fitness and whether we would cope, but we have proved that we are a competitive nation," he said.
"You know the areas we need to work on and I feel positive that the programme we had in place was a good one and that’s something I’ll take forward with me.
“You really learn that at the top level that every little thing counts. If you make mistakes the big boys will punish you and that’s what happened to us.”
Fiji also had to contend with short turnarounds, playing England, Australia and Wales in the space of 13 days.
"When you look at the scheduling, you do wonder if this benefits one team more than another; certainly it looked like the bigger teams were playing smaller countries in their short turnaround times,” McKee said.
(Reporting by Ed Osmond; Editing by David Goodman)
