England face Senegal in the round of 16 on Sunday with Rice suggesting his teammates are keen to emulate the feel-good factor created by last summer's run to the Euro 2020 final and the Lionesses' European Championship victory earlier this year.
Asked about the prospects of another deep run in Qatar lifting a nation's spirits amid high energy prices and a series of strikes over working conditions, Rice said on Thursday: "I felt that during the Euros.
"It was obviously Covid back then so we couldn't see anyone, friends or family. But we saw videos of the fans back home, I feel like that it what we've done as a team -- really brought the fans together.
"We saw the Lionesses doing it in the summer, you see the support we've got in the fan parks, in pubs and it makes me happy seeing videos of the fans after we've scored. We will try to keep going, try to lift everyone, it's obviously really close to Christmas now so hopefully we'll give them the best Christmas present.
"I think other nations will always look at us and think about the quality we've got in the squad. Why should we not be feared? If you look at our attacking players, there are world class, unbelievable talents across the board, across the whole team.
"There are players who have played in the biggest games, won the biggest trophies. We are one of the biggest teams here. But it's down to us to prove it on the pitch.
"Obviously teams like the French have proved that. They've won a World Cup. They've done it consistently. Now we want to change that. All those big nations, we want to show them we're here. We're not just here to get into the round of 16. We want to go the whole way."
Having been surrounded in camp by England players winning trophies at club level, Rice also hinted that his domestic future could lie away from West Ham if they cannot compete for the game's biggest prizes.
The midfielder has been repeatedly linked with a move to Chelsea and Manchester United among others, although the Hammers are reluctant to sell and Rice is under contract until 2024 with the club holding an option for a further year.
West Ham enjoyed two high-flying seasons under David Moyes in which they finished sixth and then seventh, reaching last year's Europa League semifinal but are currently 16th in the Premier League after winning just four of their 15 games this season.
"One hundred percent, I want to play in the Champions League," Rice said.
"For the last two or three years I've been saying that. I've been playing consistently well for club and I feel like I really want to keep pushing. I see my friends here, who are playing Champions League and for big trophies.
"You only get one career and at the end you want to look back at what you've won and the biggest games you've played in. I really want to do that."
Rice went on to reveal England's secret World Cup mascot: singer Chesney Hawkes.
The 51-year-old sang his biggest hit "The One and Only" at half-time during England's 3-0 win over Wales on Tuesday and was pictured embracing with Rice -- while wearing a "Rice 4" shirt -- at the end of the game.
"I knew the song but I actually didn't know who he was -- that is me speaking honestly," Rice said.
"He has a really familiar face, it is funny because I walked into the changing room and one of the kit men told me Chesney Hawkes was outside with my shirt on -- I was like 'I don't know who he is!'
"Then I saw he had the Rice shirt on and after the game I went and spoke to him and gave him a hug and I heard he performed at half-time and it was really good so yeah, me and Chesney are pals now!
"Is he our lucky mascot now? Yeah, I hope so. We have got to get him to the games, we won one comfortably with him there so we will get him singing 'The One and Only' at every half-time and hopefully we will get him back to number one as well."