The Dutch striker sealed a £24 million move from Arsenal on August 15, and after making an appearance in the 1-0 defeat to Everton, he got United's first in his home debut, and says that he and his team-mates will gain a good understanding as he gains fitness.
"Honestly, I have to say, from day one, everyone is making me feel at home," Van Persie told Sky Sports News. "All the players have been very nice to me, the staff, the people, the fans as well.
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"Of course, it's only a week, so we have to get used to each other a bit more in the next week, but it will happen. But honestly, I feel at home. I feel fine, everyone is helping me. I try to do that as well with the other guys.
"We have good, proper sessions every day in training so we can get used to each other - they have to get used to me, I have to get used to them, but it is going well.
"We have to give me a little bit more time personally to get match fit, because it was my first game in a long time. And after that we have to get used to each other more, and I'm very confident that will happen."
Van Persie also discussed the win over Fulham, stating that the main thing to take from the match was the three points, but that he was pleased to get an early goal at Old Trafford.
He added: "[The home debut was] very good. We got all three points, which is the main thing, it's what we're here for, and I scored a good goal. It's always good to score an early goal on your debut.
"It was a good goal, a difficult goal because it was a good cross from [Patrice] Evra, but it bounced before me so I had to time it well, which I did.
"Most of those shots go over or wide because it was a very tight angle, but luckily enough today it went in."