Bournemouth boss Howe hailed midfielder Arter's all-action showing that underpinned the Cherries' 6-1 hammering of Hull, then tipped the 26-year-old for further Ireland honours.
Arter has recently brushed off suggestions he would aim to declare for England given he has yet to feature for Ireland in a competitive fixture despite winning three caps.
The Bournemouth midfielder left Dean Court on crutches after suffering a knee problem on Saturday, but that was thought to be a precaution.
"I think the players' performance will dictate what happens on that side," said Howe of Arter's international chances.
"They've got to get their Bournemouth form right first and the rest will follow.
"When you talk about Harry the last few weeks he's been absolutely terrific for us.
"So I'm sure if he continues that form he'll get rewarded.
"We've got some very good footballers here and some very intelligent footballers.
"The way we play, it's not easy, it's the hardest way to play I believe.
"So there's a lot of responsibility on their shoulders, but they take that very well."
Junior Stanislas bagged a brace with Steve Cook, Charlie Daniels, Callum Wilson and Dan Gosling all also on target as Bournemouth ran riot against hapless Hull.
Cherries boss Howe was refusing to get carried away by either the victory or the performance however, despite Bournemouth bossing possession in total vindication of his eye-catching gameplan.
Stanislas laid on two goals as well as finding the net twice himself, leaving Howe impressed with the former West Ham winger's recent performances.
"He's in a really good run of form right now Junior," said Howe.
"He hit the woodwork last week from a free-kick and he did that again today.
"He took his goals well and his overall performance was good.
"I'm really pleased with how he's developing as a footballer."
Hull only had Ryan Mason's heavily deflected goal to show for their efforts, leaving boss Mike Phelan to issue a heavy warning on his side's Premier League future.
Robert Snodgrass' reckless challenge on Wilson gifted Bournemouth the penalty that put the hosts 3-1 to the good at the break and killed the contest.
Phelan though refused to criticise the former Norwich forward despite that almost inexplicable tackle.
"If you look at every goal there's a problem there to pick up on," said Phelan.
"One incident doesn't really change the way the game panned out.
"I'm not going to look at that for a moment
We have to do better as a group.
"I put myself in that, simply because I picked the team, the tactics and probably we didn't execute it as well as we should have done.
"It's extremely tough right now
Nobody wants the results we've been having over the past few games but that's the Premier League.
"You go into games positive and within seconds it can change.
"We'll have to look at the situation, take stock, learn from that and move on quickly."
Source : PA