The Internationals have beaten the U.S. only once in nine editions of the Ryder Cup-style event, losing all four of the most recent encounters, and need to make this week "very competitive," according to Price.
"All of us who've been involved in the Presidents Cup know how important this one is," International captain Price said during a news conference at Muirfield Village Golf Club on Tuesday where both teams were practising.
"I wouldn't say it's a must-win. That's a hard thing to put on anyone. But this one needs to be competitive.
"More important than anything else, this Presidents Cup needs to be very competitive because the last four ... I honestly believe they have not been that competitive."
Price represented the Internationals in the first five Presidents Cups, including 1998 in Melbourne when the U.S. were beaten and 2003 in South Africa when the trophy was shared.
"When we started out with the Presidents Cup, the initial guys, myself and Greg (Norman) and Ernie (Els), we so enjoyed watching the Ryder Cup and so wanted to be a part of the Ryder Cup-type format," said former world number one Price.
"And then the Presidents Cup came along and that was fantastic. The first couple were pretty exciting but as we have seen in the last decade, since 2003, it just has not been as competitive as we would like.
"And you can debate why; there's many reasons. But for all of us, this is a really big week."
As he and his team prepare for a big week at Muirfield Village, Price was delighted to report that former British Open champion Louis Oosthuizen was fully fit after being sidelined for two months by a neck-related injury.
"Louis is 100 percent," three-times major winner Price said of the South African who only returned to competition at last week's Alfred Dunhill Links Championship in Scotland where he missed the cut after three rounds.
"He played at the Dunhill last week in cool temperatures, and that's always hard when you're coming back from an injury, to play in cool temperatures. He missed the cut but he said he played really well and he didn't have any pain.
"I think the warmth this week will help him a little bit more. He's hit balls and he practised for probably a week-and-a-half before he went to the Dunhill. He's going to be ready."
Price and his opposite number, U.S. captain Fred Couples, will on Wednesday announce their pairings for Thursday's fourball matches but likely combinations were already shaping up on the first day of official practice.
Good friends Oosthuizen and Charl Schwartzel were the first group to tee off in practice on Tuesday, followed by Australian Jason Day and Canadian Graham DeLaet and then South Africans Richard Sterne and Branden Grace.
Cup veteran Els was paired up with Zimbabwean rookie Brendon de Jonge, Masters champion Adam Scott of Australia played with Japan's Hideki Matsuyama and Argentina's Angel Cabrera linked up with Australian Marc Leishman.
"With the dynamics of our team, with guys from all over the place, probably the first time all of them have ever been in one room together was last night, so it was a good evening," Price said of the Internationals' first team meeting on site.
"Just trying to find out from the guys who they felt they wanted to play with, who they would be comfortable playing with ... I got a lot of good feedback from the guys on that. They were pretty sure about who they wanted to play with.
"Obviously with the six Southern Africans, that was easy, because a lot of them had played amateur golf together and had played alternate-shot in some four ball golf over the years."
- Sports & Recreation
- Presidents Cup
- Muirfield Village Golf Club