I would take out “relative to” because it obfuscates meaning and lends nothing to the sentence.

I would take out ” to make sure” and replace it with

“verify.” Why use 3 words when you can use one?

I would also make verify that the word “objective” is definitely what you mean. If “objection” was meant, it completely changes the meaning.

You could change “a balance between demand and supply” to “a balance between supply and demand”. There’s no GREAT reason for flipping it except that normally the term is “supply and demand.” It isn’t quite an idiom, but it is more commonly phrased that way. I’d only use demand and supply if i wanted to bring special attention to the fact that I flipped the phrase.

We would not say on the world market but IN the world market. (another idiom.)

I would also remove “particularly” because I don’t think it adds to the sentence.

Their objective is not the oil price itself as many people think, but rather to verify that there is a balance between demand and supply in the world market. The current phase of rising oil prices began in 2004 due to strong demand from countries like China and the United States.

OR

Their objective is not relative to the oil price itself, as many people think, but rather to make sure that there is a balance between demand and supply in the world market. The current phase of rising oil prices began in 2004 due to strong demand, particularly from countries like China and the United States